201701FULLISSUE

ISSN 0002-9920 (print)
ISSN 1088-9477 (online)
January 2017
Volume 64, Number 1
JMM 2017 Lecture Sampler
page 8
Hodge Theory of Matroids
page 26
Donald St. P. Richards
Charleston Meeting
page 80
Gigliola Staffilani
2017 Mathematical Congress
of the Americas (MCA 2017)
page 88
Barry Simon
Tobias Holck Colding
Lisa Jeffrey
Ingrid Daubechies
Alice Silverberg
Anna Wienhard
Wilfrid Gangbo

AMERICAN MATHEMATICAL SOCIETY
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A MERICAN M ATHEMATICAL S OCIETY
CURRENT EVENTS BULLETIN
Friday, January 6, 2017, 1:00 PM to 5:00 PM
Imperial Ballroom A, Marquis Level, Marriott Marquis Atlanta
Joint Mathematics Meetings, Atlanta, GA
1:00 PM
Lydia Bieri, University of Michigan
Black hole formation and stability:
a mathematical investigation.
Mathematics seems to be the only way to shed
light on the weirdness of the universe.
2:00 PM
Matt Baker, Georgia Tech
Hodge Theory in Combinatorics.
Ideas from complex analytic geometry solve a
beautiful old problem in combinatorics.
3:00 PM
Kannan Soundararajan, Stanford University
Tao's work on the Erdős
Discrepancy Problem.
Analysis and number theory to the rescue to
understand sequences.
4:00 PM
Susan Holmes, Stanford University
Statistical proof and the
problem of irreproducibility.
Why medical (and other scientific) “results”
seem to degrade with time—and what to do
about it.
Organized by David Eisenbud,
University of California, Berkeley

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Notices
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FROM THE EDITORS
Diversity in Mathematics
EDITOR-IN-CHIEF
Frank Morgan
ASSOCIATE EDITORS
Benjamin Braun
Alexander Diaz-Lopez
Thomas Garrity
Joel Hass
Stephen Kennedy
Florian Luca
Steven J. Miller
Harriet Pollatsek
Carla Savage (ex officio)
Cesar E. Silva
Christina Sormani
Daniel J. Velleman
Recent studies of the lack of women authors and editors in prominent journals 1
raise serious concerns about the state of mathematics, but a review of the past year's
Notices reveals many positive signs for women and minorities:
The January cover featured nine Joint Meetings Invited Speakers, seven of whom
were women or minorities. The same issue featured the seven Trjitznsky Memorial
Award winning undergraduates, six of whom were women.
The February issue featured African-American NFL lineman John Urschel, an MIT
math PhD student.
The March issue featured an interview with Elisenda Grisby, associate professor
at Boston College, who won the inaugural AWM-Joan and Joseph Birman Research
Prize.
The April cover story on "Gauge Invariance of Degenerate Riemannian Metrics"
was by Alice Barbara Tumpach of Lille. The AMS Spring Sectional lecture sampler
included Laura Felicia Matusevich, Ricardo Bañuelos, and Steph van Willigenburg. In
the Graduate Student Section, Alexander Diaz-Lopez interviewed African-American
Duke mathematician Arlie Petters, a pioneer in the mathematical theory of gravitational
lensing.
The May and August interviews featured Wisconsin mathematician Melanie Wood,
an American Institute of Mathematics Five-Year Fellow, and Helen Moore, Associate
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CONSULTANTS
John Baez
Hélène Barcelo
Ricardo Cortez
Jerry Folland
Tara Holm
Kenneth A. Ribet
January 2016
JMM 2016 Lecture Sampler
page 7
The Graduate Student
Section
page 23
of the American Mathematical Society
Kristin Estella Lauter
Volume 63, Number 1
Marta Lewicka
William P. Thurston,
1946—2012, Part II
Daniel Alan Spielman
SENIOR WRITER/
DEPUTY EDITOR
page 31
Athens Meeting
page 94
Mohammad Reza Pakzad
2015 Trjitzinsky Awardee,
Kiyon Hahm
Allyn Jackson
Stony Brook Meeting
page 98
Salt Lake City Meeting
Tanya A. Moore
page 102
Tatiana Toro
MANAGING EDITOR
Karen E. Smith
Steve Zelditch
Rachel L. Rossi
Panagiota Daskalopoulos
Alex Eskin
About the cover: Seattle Speakers (see page 55)
Notices of the AMS, January 2016
Arlie Petters
4 Notices of the AMS Volume 64, Number 1

FROM THE EDITORS
John Urschel
Moon Duchin
In honor of
Hispanic Heritage Month
(September 15–October 15)
a personal vignette will be posted
by the authors of this piece at
the website Lathisms.org.
“Lathisms” is a word that stands
for Latin@s (that is, Latinos
and Latinas) and Hispanics in
the mathematical sciences.
Alice Barbara Tumpach Mei Kobayashi
Hispanic Heritage Month, October 2016
Director of Quantitative Clinical Pharmacology at Bristol-Myers
Squibb.
The September cover story, "Counting in Groups," was
by Tufts mathematician Moon Duchin. The same issue
carried a review by Mei Kobayashi of NTT Communications
of My Search for Ramanujan; "Snapshots of Modern Mathematics
from Oberwolfach" by Carla Cederbaum, Andrew
Cooper, Jürg Kramer, and Anna-Maria von Pippich; and
a story on the new AMS Executive Director, Catherine A.
Roberts. Incidentally, the outgoing chair of the AMS Board
of Trustees was Ruth Charney and the new chair is Karen
Vogtmann.
An October cover story on “Lathisms: Latin@s and
Hispanics in the Mathematical Sciences” by Alexander
Diaz-Lopez, Pamela E. Harris, Alicia Prieto Langarica, and
Gabriel Sosa pictured 24 Hispanic/Latin@ mathematicians,
featured daily on social media for Hispanic Heritage
Month. The same issue contained “Disruptions of the
Academic Math Employment Market” by Amy Cohen and
“Joining Forces in International Mathematics Outreach
Efforts” by Diana White and Alessandra Pantano.
November had a Doceamus piece, “Todos Cuentan:
Cultivating Diversity in Combinatorics,” by Federico Ardila-Mantilla
and a lecture sampler by Tulane mathematician
Ricardo Cortez.
December had a conversation with Helen G. Grundman,
new AMS Director of Education and Diversity; an interview
of Karen Saxe, new director of the AMS Washington Office;
and an opinion piece on mathematical software by Lisa
R. Goldberg.
And more, with more to come.
The new Notices Editorial Board for 2016 included for
the first time a graduate student, Alexander Diaz-Lopez,
and we also added an additional board of Consultants.
Notices is grateful for the varied contributions from our
growing mathematical family.
1 The Effect of Gender in the Publication Patterns in Mathematics by Helena Mihaljevi-Brandt,
Lucía Santamaría, and Marco Tullne, PLOS ONE, http://dx.doi.
org/10.1371/journal.pone.0165367; Measuring Gender Representation on Editorial
Boards in the Mathematical Sciences by Andrew J. Bernoff and Ursula Whitcher, SIAM
News, November, 2016, https://sinews.siam.org/DetailsPage/TabId/900/
ArtMID/2243/ArticleID/1716/Measuring-Gender-Representation-on-Editorial-Boards-in-the-Mathematical-Sciences.aspx;
Gender Representation on
Journal Editorial Boards in the Mathematical Sciences by Chad M. Topaz and Shilad
Sen, arXiv.org (2016), https://arxiv.org/abs/1606.06196.
January 2017 Notices of the AMS 5

Notices
of the American Mathematical Society
FEATURES
January 2017
8 32
26
JMM 2017 Lecture Sampler
Barry Simon, Alice Silverberg, Lisa
Jeffrey, Gigliola Staffilani, Anna
Wienhard, Donald St. P. Richards,
Tobias Holck Colding, Wilfrid Gangbo,
and Ingrid Daubechies
The Graduate Student
Section
Interview with Arthur Benjamin
by Alexander Diaz-Lopez
WHAT IS?...a Complex Symmetric
Operator
by Stephan Ramon Garcia
Graduate Student Blog
Hodge Theory of
Matroids
Karim Adiprasito, June Huh, and
Eric Katz
Enjoy the Joint Mathematics Meetings from near or afar through our lecture sampler and our feature on Hodge Theory,
the subject of a JMM Current Events Bulletin Lecture. This month's Graduate Student Section includes an interview
with Arthur Benjamin, "WHAT IS...a Complex Symmetric Operator?" and the latest "Lego Graduate Student" craze.
The BackPage announces the October caption contest winner and presents a new caption contest for January.
As always, comments are welcome on our webpage. And if you're not already a member of the AMS, I hope you'll consider
joining, not just because you will receive each issue of these Notices but because you believe in our goal of supporting
and opening up mathematics.
—Frank Morgan, Editor-in-Chief
ALSO IN THIS ISSUE
40 My Year as an AMS Congressional Fellow
Anthony J. Macula
44 AMS Trjitzinsky Awards Program Celebrates Its
Twenty-Fifth Year
47 Origins of Mathematical Words
A Review by Andrew I. Dale
54 Aleksander (Olek) Pelczynski, 1932–2012
Edited by Joe Diestel
73 2017 Annual Meeting of the American Association for
the Advancement of Science
Matroids (top) and Dispersion in a Prism (bottom), from this month's
contributed features; see pages 8 and 26.

Notices
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96 The Back Page
Gallery of the Infinite
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Barry Simon, Alice Silverberg, Lisa Jeffrey, Gigliola Staffilani, Anna Wienhard, Donald St. P. Richards, Tobias Holck Colding, Wilfrid Gangbo,
and Ingrid Daubechies.
page 8
— Barry Simon, “Spectral Theory Sum Rules, Meromorphic Herglotz
Functions and Large Deviations”
10:05 am–10:55 am, Wednesday, January 4.
page 10 — Alice Silverberg, “Through the Cryptographer’s Looking-Glass, and What
Alice Found There”
11:10 am–12:00 pm, Wednesday, January 4.
page 12 — Lisa Jeffrey, “The Real Locus of an Antisymplectic Involution”
10:05 am–10:55 am, Thursday, January 5.
page 12 — Gigliola Staffilani, “The Many Faces of Dispersive and Wave Equations”
2:15 pm–3:05 pm, Thursday, January 5.
page 15 — Anna Wienhard, “A Tale of Rigidity and Flexibility—Discrete Subgroups of
Higher Rank Lie Groups”
10:05 am–10:55 am, Friday, January 6.
page 16 — Donald St. P. Richards, “Distance Correlation: A New Tool for Detecting
Association and Measuring Correlation between Data Sets”
11:10 am–12:00 pm, Friday, January 6.
page 18 — Tobias Holck Colding, “Arrival Time”
9:00 am–9:50 am, Saturday, January 7.
page 19 — Wilfrid Gangbo, “Paths of Minimal Lengths on the Set of Exact k-forms”
1:00 pm–1:50 pm, Saturday, January 7.
page 20 — Ingrid Daubechies, “Reunited: Francescuccio Ghissi’s St. John Altarpiece”
3:00 pm–3:50 pm, Saturday, January 7.
page 23 — Biographies of the Speakers
8 Notices of the AMS Volume 64, Number 1

Barry Simon
Spectral Theory Sum Rules, Meromorphic
Herglotz Functions and Large Deviations
Almost exactly forty years
ago, Kruskal and collaborators
revolutionized significant
parts of applied mathematics
by discovering remarkable
structures in the KdV equation.
Their main discovery
was that KdV is completely
integrable with the resulting
infinite number of conservation
laws, but deeper aspects
concern the connection to the
1D Schrödinger equation
Barry Simon received
the 2016 Steele Prize
for Lifetime
Achievement and was
featured in the 2016
August and September
issues of Notices.
(1) − d2
dx 2 + V(x)
where the potential, V, is
actually fixed time data for
KdV.
In particular, the conserved
quantities which are integrals
of polynomials in V and its derivatives can also be
expressed in terms of spectral data. Thus one gets a sum
rule, an equality between coefficient data on one side and
spectral data on the other side. The most celebrated KdV
sum rule is that of Gardner et al.:
(2)
1
π ∫∞ 0
log |t(E)| −1 E 1/2 dE + 2 3 ∑ n
|E n | 3/2 = 1 8 ∫∞ −∞
V(x) 2 dx
where {E n } are the negative eigenvalues and t(E) the
scattering theory transmission coefficient. We note that
in this sum rule all terms are positive.
While these are well known, what is not so well known
is that there are much earlier spectral theory sum rules,
which, depending on your point of view, go back to 1915,
1920, or 1936. They go under the rubric Szegő’s Theorem,
which expressed in terms of Toeplitz determinants goes
back to 1915. In 1920 Szegő realized a reformulation
in terms of norms of orthogonal polynomials on the
unit circle (OPUC), but it was Verblunsky in 1936 who
first proved the theorem for general measures on ∂D
(={z ∈ C | |z| = 1})—Szegő had it only for purely a.c.
measures—and who expressed it as a sum rule.
To explain the sum rule, given a probability measure, μ,
on ∂D which is nontrivial (i.e. not supported on a finite
Barry Simon is I.B.M. Professor of Mathematics and Theoretical
Physics, Emeritus, at Caltech. His e-mail address is bsimon@
caltech.edu.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1461
set of points), let {Φ n (z)} ∞ n=0 be the monic orthogonal
polynomials for μ. They obey a recursion relation
(3)
Φ n+1 (z) = zΦ n (z) − α n Φn ∗ (z); Φ 0 ≡ 1; Φn ∗ (z) = z n Φ n ( 1̄ z )
where {α n } ∞ n=0 are a sequence of numbers, called Verblunsky
coefficients, in D. μ ↦ {α n } ∞ n=0 sets up a 1-1
correspondence between nontrivial probability measures
on D and D ∞ .
The Szegő-Verblunsky sum rule says that if
(4) dμ(θ) = w(θ) dθ
2π + dμ s
then
(5) ∫ log(w(θ)) dθ ∞
2π = − ∑ log(1 − α n | 2 )
n=0
In particular, the condition that both sides are finite at
the same time implies that
(6)
∞
∑ |α j | 2 < ∞ ⟺ ∫ log(w(θ)) dθ
j=0
2π > −∞
Simon [3] calls a result like (6) that is an equivalence
between coefficient data and measure theoretic data a
spectral theory gem.
In 2000 Killip and I found an analog of the Szegő-
Verblunsky sum rule for orthogonal polynomials on the
real line. One now has nontrivial probability measures
on R, and {p n } ∞ n=0 are orthonormal polynomials whose
recursion relation is
(7)
xp n (x) = a n+1 p n+1 (x)+b n+1 p n (x)+a n p n−1 (x); p −1 ≡ 0
where the Jacobi parameters obey b n ∈ R, a n ≥ 0. There
is now a bijection of nontrivial probability measures of
compact support on R and uniformly bounded sets of
Jacobi parameters (Favard’s Theorem).
If
(8) dμ(x) = w(x)dx + dμ s
then the gem of Killip-Simon says that
(9)
∞
∑
n=1
(a n − 1) 2 + b 2 n < ∞
⟺
ess supp (dμ)=[−2, 2], Q(μ)2
F(E n ) =
∞
∑
n=1
[ 1 4 b2 n + 1 2 G(a n)]
January 2017 Notices of the AMS 9

where
(12)
F(β + β −1 ) = 1 4 [β2 + β −2 − log(β 4 )], β ∈ R\[−1, 1]
(13)
G(a) = a 2 − 1 − log(a 2 )
The gem comes from G(a) > 0 on (0, ∞)\{1}, G(a) =
2(a − 1) 2 + O((a − 1) 3 ), F(E) > 0 on R\[−2, 2], F(E) =
2
3
(|E| − 2) 3/2 + O((|E| − 2) 5/2 ). To get gems from the sum
rule without worrying about cancellation of infinities, it
is critical that all the terms are positive.
This situation
changed
dramatically
in the
summer of
2014
It was mysterious why there
was any positive combination
and if there was any meaning
to the functions G and F which
popped out of calculation and
combination. Moreover, the
weight (4 − x 2 ) 1/2 was mysterious.
Prior work had something
called the Szegő condition with
the weight (4−x 2 ) −1/2 , which is
natural, since under x = 2 cos θ
one finds that (4 − x 2 ) −1/2 dx
goes to dθ up to a constant.
This situation remained for almost fifteen years, during
which period there was considerable follow-up work
but no really different alternate proof of the Killip-Simon
result. This situation changed dramatically in the summer
of 2014 when Gamboa, Nagel, and Rouault [1] (henceforth
GNR) found a probabilistic approach using the theory of
large deviations from probability theory.
Their approach shed light on all the mysteries. The
measure (4 − x 2 ) 1/2 dx is just (up to scaling and normalization)
the celebrated Wigner semicircle law for the
limiting eigenvalue distribution for GUE. The function G
of (13) is just the rate function for averages of sums of
independent exponential random variables, as one can
compute from Cramér’s Theorem, and the function F
of (12) is just the logarithmic potential in a quadratic
external field which occurs in numerous places in the
theory of random matrices.
In the first half of my lecture, I’ll discuss sum rules via
meromorphic Herglotz functions and in the second half
the large deviations approach of GNR.
References
[1] F. Gamboa, J. Nagel, and A. Rouault, Sum rules via large
deviations, J. Funct. Anal. 270 (2016), 509–559. MR3425894
[2] R. Killip and B. Simon, Sum rules for Jacobi matrices and
their applications to spectral theory, Ann. Math. 158 (2003),
253–321. MR1999923
[3] B. Simon, Szego’s Theorem and Its Descendants: Spectral Theory
for L 2 Perturbations of Orthogonal Polynomials, Princeton
University Press, Princeton, NJ, 2011. MR2743058
Alice Silverberg
Through the Cryptographer’s Looking-Glass,
and What Alice Found There
Mathematicians and
cryptographers have
much to learn from
one another. However,
in many ways
they come from different
cultures and
don’t speak the same
language. I started
as a number theorist
and have been
welcomed into the
community of cryptographers.
Through joint
research projects and
conference organizing,
I have been working to
help the two communities
Alice Silverberg
play well together
and interact more. I
have found living and working in the two worlds of
mathematics and cryptography to be interesting, useful,
and challenging. In the lecture I will share some thoughts
on what I’ve learned, both scientifically and otherwise.
A primary scientific focus
of the talk will
Can more than be on the quest for a
Holy Grail of cryptography,
three parties
namely, cryptographically
efficiently create
useful multilinear maps.
Suppose that Alice and
a shared secret? Bob want to create a shared
secret, for example to use
as a secret key for encrypting a credit card transaction,
but their communication channel is insecure. Creating a
shared secret can be done using public key cryptography,
as follows. Alice and Bob fix a large prime number p
and an integer g that has large order modulo p. Alice
then chooses a secret integer A, computes g A mod p, and
sends it to Bob, while Bob similarly chooses a secret B and
sends g B mod p to Alice. Note that Eve, the eavesdropper,
might listen in on the transmissions and learn g A mod p
and/or g B mod p. Alice and Bob can each compute their
Alice Silverberg is professor of mathematics and computer science
at the University of California, Irvine. Her e-mail address is
asilverb@math.uci.edu.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1453
10 Notices of the AMS Volume 64, Number 1

Can Alice, through the cryptographer’s looking glass,
find an efficient way for many parties to create a
shared secret key?
shared secret g AB mod p, Alice computing (g B mod
p) A mod p and Bob computing (g A mod p) B mod p. It’s
a secret because it is believed to be difficult for Eve
to compute g AB mod p when she knows g A mod p and
g B mod p but not A or B (this belief is called the
Diffie-Hellman assumption). This algorithm is known as
Diffie-Hellman key agreement.
Can more than two parties efficiently create a shared
secret? It’s a nice exercise to think about why naïvely
extending the above argument doesn’t work with only
one round of broadcasting (in the above, the broadcasting
consists of Alice sending g A mod p, while Bob sends
g B mod p).
Here’s an idea for how n + 1 people could create a
shared secret. Suppose we could find finite cyclic groups
G 1 and G 2 of the same size and an efficiently computable
map
e ∶ G n 1 → G 2
such that (with g a generator of G 1 ):
(a) e(g a1 , … , g an ) = e(g, … , g) a1⋯an for all integers
a 1 , … , a n (multilinear),
(b) e(g, … , g) is a generator of G 2 (nondegenerate), and
(c) it is difficult to compute e(g, … , g) a1⋯an+1
when
a 1 , … , a n+1 are unknown, even given g a1 , … , g an+1
(the multilinear Diffie-Hellman assumption).
A multilinear version of Diffie-Hellman key agreement
would go as follows. Alice chooses her secret integer
a 1 and broadcasts g a1 , Bob chooses his secret a 2 and
broadcasts g a2 , …, and Ophelia chooses her secret a n+1
and broadcasts g an+1 . Then all n + 1 people can compute
the group element e(g, … , g) a1⋯an+1 ; for example, Bob
computes e(g a1 , g a3 , … , g an+1 ) a2 . By (c), it’s hard for anyone
else to learn this group element. In this way, n + 1 people
Mathematicians and cryptographers at a 2015
conference on the Mathematics of Cryptography.
can create a shared secret. When n = 1 and e is the
identity map on a (large) subgroup of the multiplicative
group of the finite field with p elements, this is the
Diffie-Hellman key agreement algorithm described above,
which allows two parties to share a secret. For three
parties, such maps e can be constructed from pairings
(n = 2) on elliptic curves. For more than three parties,
finding such cryptographically useful multilinear maps e
is a major open problem in cryptography and an area of
current research.
In [1], Dan Boneh and I raised this question; gave
applications to broadcast encryption, digital signatures,
and key agreement; and gave evidence that it would be
difficult to find very natural mathematical structures,
like “motives,” giving rise to such maps e when n > 2.
(As my coauthor generously allowed me to include in
the introduction to our paper, “We have the means and
the opportunity. But do we have the motive?”) Events
since then have led us to become more optimistic that a
creative solution can be found, and we are hopeful that the
combined efforts of mathematicians and cryptographers
will lead to progress on this problem.
References
[1] Dan Boneh and Alice Silverberg, Applications of multilinear
forms to cryptography, in Topics in Algebraic
and Noncommutative Geometry: Proceedings in Memory
of Ruth Michler, Contemporary Mathematics 324, American
Mathematical Society, Providence, RI, 2003, pp. 71–90.
MR1986114
January 2017 Notices of the AMS 11

Lisa Jeffrey
The Real Locus of an Antisymplectic
Involution
Suppose M is a compact symplectic
manifold equipped
with an antisymplectic involution.
Then the fixed point
set of the involution is a
Lagrangian submanifold.
A prototype example is
complex projective space
CP n , with the involution complex
conjugation. The fixed
point set of the involution
is then real projective space
RP n . In the case n = 1, CP 1
is the same as the 2-sphere
S 2 , and the fixed point set of
Lisa Jeffrey
the involution is the equator
(which is RP 1 , which is a circle).
Suppose in addition M has a Hamiltonian torus action. It
is possible to define what it means for the torus action to
be compatible with the involution. In the above example,
the torus action is the standard action of U(1) n on CP n .
(For n = 1 this is the rotation action of U(1) rotating
around the vertical axis.)
In 1983 Hans Duistermaat [1] proved many results in
this situation, among them that the image of the moment
map restricted to the fixed point set of the involution is the
same as the image of the moment map for the symplectic
manifold (in particular it is a convex polyhedron, as shown
by Atiyah and Guillemin-Sternberg).
Numerous symplectic manifolds fit into this picture. In
particular some character varieties (spaces of conjugacy
classes of representations of the fundamental group) are
naturally equipped with Hamiltonian torus actions. Jeffrey
and Weitsman [2] developed Hamiltonian torus actions
on open dense subsets in SU(2) character varieties for
orientable 2-manifolds, following a groundbreaking 1986
article by Goldman that describes Hamiltonian flows of a
natural class of functions on these character varieties.
References
[1] J.J. Duistermaat, Convexity and tightness for restrictions
of Hamiltonian functions to fixed point sets of an antisymplectic
involution. Trans. Amer. Math. Soc. 275 (1983), no. 1,
417–429. MR678361
Lisa Jeffrey is professor of mathematics at the University of Toronto.
Her e-mail address is jeffrey@math.toronto.edu.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1456
[2] L. Jeffrey and J. Weitsman, Bohr-Sommerfeld orbits in the
moduli space of flat connections and the Verlinde dimension
formula. Commun. Math. Phys. 150 (1992), no. 3, 593–630.
MR1204322
Gigliola Staffilani
The Many Faces of Dispersive and Wave
Equations
One of the most
beautiful effects
of dispersion is
a rainbow, as in
Figure 1, or, more
prosaically, the refraction
of a ray
of light through
a prism, as in
Figure 2.
While looking at
this timeless phenomenon
it is
Gigliola Staffilani
hard to believe it
is connected to
Vinogradov’s Mean Value Theorem, one of several deep
theorems in number theory. The mathematical nature
of dispersion is the starting point of a very rich mathematical
activity that has seen incredible progress in the
last twenty years and that has involved many different
branches of mathematics: Fourier and harmonic analysis,
analytic number theory, differential and symplectic
geometry, dynamical systems and probability. It would
take a very long book to explain all these interactions and
consequences, so here we just give a small sample, which
we hope can still suggest the wealth of what has been
accomplished and what is still there to discover.
Let us start with one of the best-known equations of
dispersive type, the nonlinear Schrödinger equation (NLS),
the quantum analog of Newton’s F = ma. We consider
the Cauchy problem: that is, given initial data u(0, x) at
time t = 0:
(1) { i∂ tu + Δu = λu|u| 2 ,
u(0, x) = u 0 (x),
where λ = ±1 and x ∈ R 2 . If we want a periodic solution,
then we take x ∈ T 2 , the torus of dimension two. Usually
we measure the smoothness of the initial data by assuming
that it is in a Sobolev space of order s, that is, u 0 ∈ H s . This
problem plays a fundamental role in physics that we will
not discuss here, but certainly once the Cauchy problem
Gigliola Staffilani is the Abby Rockefeller Mauze Professor of Mathematics
at MIT. Her e-mail address is gigliola@mit.edu.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1459
12 Notices of the AMS Volume 64, Number 1

Figure 1. An Alaskan rainbow.
where S(t) is the Schrödinger group and S(t)u 0 (x) is
the linear solution with initial data u 0 . Since H 1 and in
particular L 2 are spaces of relatively low regularities, a
classical energy method based on a priori bounds such
as (2) and (3) is not enough to prove well-posedness.
An extremely efficient and successful way to show wellposedness
instead is via (4) and a fixed point method. For
this it is important to establish a function space in which
a fixed point theorem can be set up. Such a function space
is dictated by estimates for the linear solution S(t)u 0 ,
since as a first try we can think of the nonhomogeneous
term ∫ t 0 S(t−t′ )|u| 2 u(t ′ )dt ′ as a perturbation. This brings
us to the famous Strichartz estimates that in R 2 read as
(5) ‖S(t)u 0 ‖ L
q
t L p x ≤ C‖u 0‖ L 2,
where the couple (q, p) is admissible; that is, it satisfies
2
q = 2 ( 1 2 − 1 p ) .
The proof of (5) is a direct consequence of (2) and of the
dispersive estimate
(6) |S(t)u 0 (x)| ≤ C ‖u 0‖ L 1
,
|t|
which in turn follows from the explicit formula
Figure 2. The dispersion in a prism has deep
connections to number theory.
is set up one wants to prove existence and uniqueness of
solutions, together with stability properties that allow us
to say that if, for example, the initial data u 0 (x) changes
a little, then the solution changes also only a little. This
can be summarized as well-posedness of the initial value
problem. As a physical problem (1) satisfies conservation
of mass
(2) M = ∫ |u(t, x)| 2 dx
and of energy
(3) E = 1 2 ∫ |∇u(t, x)|2 dx − λ 4 ∫ |u(t, x)|4 dx.
Hence natural sets of initial data are the spaces L 2 and H 1 .
Clearly at this level of regularity not even the equation in
(1) makes sense; hence we reformulate (1) via the Duhamel
principle into the integral equation
(4) u(t, x) = S(t)u 0 (x)+λ ∫ S(t−t ′ )u(t ′ , x)|u(t ′ , x)| 2 dt ′ ,
S(t)u 0 (x) = c 1
t ∫ u |x−y|2
i c
0(y)e 2 t
dy,
where c 1 and c 2 are two given complex numbers. From (6)
we learn that in spite of the fact that the signal S(t)u 0 (x)
conserves mass, it is dispersive: its intensity dies off as
long as no obstacles or boundaries are present.
When we consider the periodic version of the problem
(1), the situation is much more subtle, because in fact
the dispersion is interrupted by the boundary conditions.
It is in this case that Bourgain used tools from analytic
number theory to prove that
(7) ‖S(t)u 0 ‖ L
4
[0,1] L 4 T 2 ≤ C‖u 0‖ Hs (T 2 ),
where T 2 is a rational torus 1 and s > 0. The main ingredient
from analytic number theory used in the proof is that
log R
on a circle of radius R there are at most expC
log R log R
many lattice points sitting on it. It took about twenty
years to obtain (7) for a generic torus. It was proved
by Bourgain and Demeter as a consequence of their
proof of the L 2 decoupling conjecture using classical
harmonic analysis tools and elements from incidence
geometry, initially introduced in this context by Guth.
Here no analytic number theory is used, quite the opposite:
Bourgain, Demeter, and Guth used harmonic analysis to
prove an outstanding conjecture related to the famous
Vinogradov’s Mean Value Theorem.
What one can prove about the global dynamics of the
problem is all linked to the focusing or defocusing nature
of the equation, respectively λ = 1 and λ = −1, and then
to the fact that (1) is mass critical, in the sense that the
1 That is, the ratio of the two periods is a rational number.
January 2017 Notices of the AMS 13

L 2 is invariant with respect to the natural scaling of the
problem. A very short analysis follows below.
The Defocusing NLS in R 2
Global well-posedness for smooth (s ≥ 1) data is a
straightforward consequence of the fact that the local
time of existence depends on the norm H s of the data
when s > 0, and when s = 1 the energy conservation (3)
bounds this norm, since λ = −1. By using the I-method,
global well-posedness can be shown for s < 1, but close to
1 serious obstructions do not allow this method to reach
L 2 . In fact, L 2 is a very special case, due to the criticality
of the problem at this level, and a global well-posedness
in L 2 was only recently proved by Dodson. This settles
completely the long-time dynamics of the problem in this
case.
The Focusing NLS in R 2
In this case, the long-time dynamics is much richer since
blowup is possible and solitons exist. It is in cases like
these that one would like to show that a generic solution
is made up by finitely many solitons and a radiation that
ultimately behaves as a linear solution. In very general
terms, this goes under the name of the Soliton Resolution
Conjecture. At the moment we are far from proving this
conjecture for the NLS, but a series of recent works by
Duyckaerts, Kenig, and Merle proved the conjecture for
certain nonlinear wave equations. On top of the usual
Strichartz estimates, a large number of new tools had
The periodic case
is much more
delicate
to be implemented in
order to obtain this
result. Among these
tools we recall the
profile decomposition,
initially introduced by
Gerard and collaborators
in order to study
the failure of compactness of Strichartz inequalities, and
channels of energy.
The question of blowup for NLS equations instead
has been studied in great detail in a series of works
by Raphäel and Merle. In an astonishing result, they
confirmed mathematically what is now known as the
log − log blow-up regime, which had been previously
numerically identified by Papanicolaou, C. Sulem, and
P.-L. Sulem.
The Defocusing NLS in T 2
As mentioned above, the periodic case is much more delicate
since boundary effects amplify the nonlinear nature
of the problem. As recalled above, using the Strichartz
estimate (7), Bourgain proved local well-posedness for
rational tori in H s for s > 0. Now that (7) is also available
for irrational tori, Bourgain’s result can be extended.
Local well-posedness in L 2 is still an open, difficult, and
extremely interesting question. Again in the defocusing
case the energy estimate (3) is enough to show global
well-posedness in H s for s ≥ 1. For rational tori also
in this case the I-method can be used to show global
well-posedness slightly below H 1 . For irrational tori this
should still hold, but no proof has been published yet. In
any case, we now know that smooth solutions are global,
and for these global solutions a very interesting and
physically meaningful problem is to study the transfer
of energy from low to high frequencies. This concept
is linked to the notion of weak turbulence and forward
cascade, on which we will not elaborate here. What we
will say, though, is that one possible way to study if such
a transfer of energy occurs is to analyze the growth in
time of the norm H s , for s large, of a smooth solution
u. So far, we know that this growth cannot be more
than polynomial. Although this result is concerned with
smooth data, the tools used to obtain it are fundamentally
based on very fine estimates of wave packets at a very low
regime of regularity. Also as of now the proofs of these
results have been presented for rational tori. One should
be able to repeat them also in the irrational case. In fact,
for irrational tori, one may expect a lower degree for the
polynomial growth, since the set of frequencies that are
in resonance, believed to be responsible for the transfer
of energy, can be proved to be smaller in the irrational
case. As for exhibiting solutions that actually have an H s
norm that grows in time at least logarithmically, at the
moment no such result is available. It has been proved,
though, by Colliander, Keel, Takaoka, Tao, and the author
of this note, with techniques that resemble those used
in dynamical systems, that there are solutions that start
small but grow arbitrarily large.
Finally, we would like to touch upon the fact that the
periodic NLS can also be viewed as an infinite-dimensional
Hamiltonian system by rewriting equation (1) for u(t, x)
as a system for its Fourier coefficients a k (t) + ib k (t) for
k ∈ Z 2 . For such a system, a Gibbs measure can be defined
with support in H −ε , and Bourgain proved that a global
NLS flow can be defined on the support of the Gibbs
measure (almost sure global well-posedness), and the
Gibbs measure ultimately can be proved to be invariant.
Note that such a result is the first in proving generically
global well-posedness in a space of supercritical regularity
with respect to the intrinsic scaling of the equation. In
order to prove this result elements of probability had to
be introduced, and many generalizations have now been
considered and not only for NLS.
Let us now conclude by introducing one last concept
associated with dispersive equations that can be
viewed as infinite-dimensional Hamiltonian systems: the
nonsqueezing theorem. In finite dimensions this is a celebrated
theorem of Gromov. It states that a Hamiltonian
flow that is also a symplectomorphism cannot squeeze a
ball into a cylinder of smaller radius. Kuksin has investigated
quite extensively how to extend this theorem to
the infinite-dimensional case. For the infinite-dimensional
Hamiltonian system associated to (1) the L 2 space can be
equipped with a symplectic structure, but unfortunately,
as recalled above, for now we do not know if a global NLS
14 Notices of the AMS Volume 64, Number 1

flow in L 2 can be defined. Nevertheless, nonsqueezing
theorems have been proved in the periodic case for the
1D cubic and NLS, for the KdV equation, and conditionally
for other systems. Moreover, recently Killip, Visan, and
Zhang proved that in the appropriate sense the global
flow for (1) in R 2 is indeed nonsqueezing.
You will not find here a section on the global dynamics
of the focusing periodic NLS, since it remains wide open.
Anna Wienhard
A Tale of Rigidity and Flexibility—Discrete
Subgroups of Higher Rank Lie Groups
In 1872 Felix Klein proposed to
approach geometry as the study
of symmetry. Instead of starting
with geometric quantites, he
considered the geometric properties
of a space to be those
that are invariant under a certain
group of transformations.
This gave a unified approach
to various geometries that had
been studied extensively in the
nineteenth century, in particular,
to classical Euclidean geometry,
spherical geometry, the newly
Anna Wienhard discovered hyperbolic geometry,
and projective geometry, the geometry
of perspective art. In fact, Klein interpreted
all three—Euclidean geometry, spherical geometry, and
hyperbolic geometry—as subgeometries of projective geometry.
Felix Klein’s approach to geometry has deeply
influenced our understanding of geometry in modern
mathematics and theoretical physics.
The key role in Klein’s approach is played by Lie groups,
which arise as continuous groups of symmetries. Examples
of Lie groups are R n (as translations of Euclidean
space E n ), invertible matrices GL(n, R), matrices of determinant
one SL(n, R), symplectic matrices Sp(2n, R),
and orthogonal matrices SO(p, q). It has since become an
important endeavor in mathematics to understand the
structure of Lie groups and also of their subgroups, in
particular, their discrete subgroups.
Discrete subgroups of Lie groups preserve additional
structure of the space. This additional structure breaks
the continuous symmetry preserved by the ambient Lie
group. For example, the group of translations R n preserves
E n with all its geometric properties. But if we consider
Anna Wienhard is a professor at Mathematisches Institut,
Ruprecht-Karls-Universität Heidelberg. Her e-mail address is
wienhard@mathi.uni-heidelberg.de.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1455
Figure 1. The group of symmetries preserving this
pattern is the lattice Z 2 in R 2 .
Figure 2. The group of symmetries preserving this
pattern in the hyperbolic Poincaré disk is a lattice in
SL(2, R).
Figure 3. The group of symmetries preserving this
circle packing is a nonlattice (“thin”) subgroup of
SO(1,3). Thin subgroups are generally harder to
understand than lattice subgroups.
inside E n the set of points with integer coordinates, then
this set of points is not preserved under translation by
an element in R n , but only by elements in the discrete
subgroup Z n . The subgroup Z n is an example of a lattice
in R n ; it has finite volume fundamental domain, namely,
the unit square. Figure 1 shows a planar pattern with
symmetry group Z 2 . Figure 2 shows a pattern in the
hyperbolic Poincaré disk with symmetry group a lattice
in SL(2, R).
January 2017 Notices of the AMS 15

Discrete subgroups also arise as monodromies of differential
equations or from geometric, dynamical, or
number-theoretic constructions. A special case of discrete
subgroups is lattices. Lattices are very “big” discrete
subgroups: they have finite covolume with respect to a
natural measure on the Lie group. Discrete subgroups
that are not lattices are sometimes called thin or small
subgroups of the Lie groups, as in Figure 3. Whereas
lattices in Lie groups are fairly well understood, it is
rather difficult to get a handle on discrete subgroups that
are not lattices.
For lattices there is a big difference between Lie groups
of rank one, which are those whose associated geometry
exhibits strictly negative curvature, and Lie groups of
higher rank, which are those whose associated geometry
exhibits only nonpositive curvature. For example, SL(n, R)
is of rank one if and only if n = 2, in which case it is
the group of symmetries of the hyperbolic plane. A series
of celebrated rigidity results of G. Margulis implies that
every lattice in a higher rank Lie group arises from a
number-theoretic construction and that many questions
about these lattices can be answered by considering the
ambient Lie group, which is much easier to understand.
Since then rigidity has been the overarching paradigm
when studying subgroups of Lie groups of higher rank. In
the rank one situation, in particular for SL(2, R), lattices
are essentially free groups or fundamental groups of
surfaces, and these groups are rather flexible. They allow
for a continuous space of deformations within SL(2, R).
In recent years new developments in geometry, lowdimensional
topology, number theory, analysis, and
representation theory have led to the discovery of several
interesting examples of discrete subgroups that are
thin (i.e., not lattices) but—quite surprisingly—admit an
interesting structure theory, which arises from a combination
of the flexibility of free groups, surface groups,
and more generally hyperbolic groups with the rigidity
of higher rank Lie groups. One particularly exciting development
is the discovery of higher Teichmüller spaces
Wienhard discusses projective deformations of a
hyperbolic 3-manifold with postdoctoral fellow
Dr. Gye-Seon Lee.
and their relation to various areas in mathematics, such
as analysis, algebraic geometry, geometry, dynamics, and
representation theory.
Donald St. P. Richards
Distance Correlation: A New Tool for Detecting
Association and Measuring Correlation
between Data Sets
The difficulties of detecting
association, measuring
correlation, and
establishing cause and
effect have fascinated
mankind since time immemorial.
Democritus,
the Greek philosopher,
emphasized well the
importance and the difficulty
of proving causality
when he wrote, “I would
rather discover one cause
than gain the kingdom of
Donald St. P. Richards
Persia.”
To address problems of relating cause and effect,
statisticians have developed many inferential techniques.
Perhaps the most well-known method stems from Karl
Pearson’s coefficient of correlation, which Pearson introduced
in the late nineteenth century based on ideas of
Francis Galton. The Pearson coefficient applies only to
scalar random variables, however, and it is inapplicable
generally if the relationship between X and Y is highly
nonlinear; this has led to the amusing enumeration of
correlations between pairs of unrelated variables, e.g.,
“Median salaries of college faculty” and “Annual liquor
sales in college towns.”
Székely et al. [3] defined a new distance covariance,
V(X, Y), and related correlation coefficient, R(X, Y).
These entities are defined for random vectors X and Y of
any dimension. Moreover, X and Y are mutually independent
if and only if R(X, Y) = 0. These properties provide
advantages of R(X, Y) over the Pearson coefficient and
other measures of correlation.
Donald St. P. Richards is professor of statistics at Penn State University.
His e-mail address is richards@stat.psu.edu.
This research was supported in part by National Science Foundation
grants AST-0908440 and DMS-1309808, and by a Romberg
Guest Professorship at the University of Heidelberg Graduate
School for Mathematical and Computational Methods in the Sciences,
funded by German Universities Excellence Initiative grant
GSC 220/2.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1457
16 Notices of the AMS Volume 64, Number 1

Figure 1. The distance correlation coefficient exhibited a superior ability to resolve astrophysical data into
concentrated horseshoe- or V-shapes and led to more accurate classification of galaxies and identification
of outlying pairs. The subplots for each galaxy type are shown in four middle frames, their superposition in
the large left frame. Potential outlying pairs in the scatter plot for Type 3 galaxies are circled in the large right
frame.
For a pair of jointly
distributed random vectors
(X, Y), it is
nontrivial to calculate
V(X, Y). Recent work
of Dueck et al. [1] calculates
V(X, Y) for the
Lancaster distributions.
The distance correlation
coefficient has
now been applied in
many contexts. It has
been found to exhibit
higher statistical
power, i.e., fewer false
positives, than the Pearson
coefficient, to find
nonlinear associations
that were undetected
by the Pearson coefficient,
and to locate
smaller sets of variables
that provide equivalent
statistical information.
The distance
correlation
coefficient has
now been applied
in many contexts.
It has been found
to exhibit higher
statistical power,
i.e., fewer false
positives, than the
Pearson
coefficient
In the field of astrophysics, large amounts of data
are collected and stored in publicly available repositories.
The COMBO-17 database, for instance, provides numerical
measurements on many astrophysical variables for more
than 63,000 galaxies, stars, quasars, and unclassified
objects in the Chandra Deep Field South region of the
sky, with brightness measurements over a wide range
of redshifts. Current understanding of galaxy formation
and evolution is sensitive to the relationships between
astrophysical variables, so it is essential in astrophysics
to be able to detect and verify associations between
variables.
Mercedes Richards et al. [2] applied the distance correlation
method to 33 variables measured on 15,352 galaxies
in the COMBO-17 database. For each of the ( 33
2 ) = 528
pairs of variables, the Pearson and distance correlation
coefficients were graphed in Figure 1 for galaxies with
redshift z ∈ [0, 0.5). We found that, for given values of
the Pearson coefficient, the distance correlation had a
greater ability than other measures of correlation to resolve
the data into concentrated horseshoe- or V-shapes.
These results were observed over a range of redshifts
beyond the Local Universe and for galaxies ranging in
type from elliptical to spiral.
The greater ability of the distance correlation to resolve
data into well-defined horseshoe- or V-shapes leads to
more accurate classification of galaxies and identification
of outlying pairs of variables. As seen in Figure 1, the
Type 2 and Type 3 groups of spiral galaxies appear to be
contaminated substantially by Type 4 starburst galaxies,
confirming earlier findings of other astrophysicists. Our
study found further evidence of this contamination from
the V-shaped scatter plots for galaxies of Type 2 or 3.
I will also explore data on the relationship between
homicide rates and the strength of state gun laws. 1
A Washington Post columnist has claimed that there is
“zero correlation between state homicide rate and state
gun laws” [4]. Although the Pearson coefficient detects
no statistically significant relationship between those
variables, a distance correlation analysis discovers strong
evidence of a relationship when the states are partitioned
by region.
1 As sure as my first name is “Donald,” this portion of the talk will
be Huge!
January 2017 Notices of the AMS 17

Distance correlation applications rest on a curious
singular integral: For x ∈ R p and 0 < Re(α) < 1,
∫
R p
1 − e i⟨s,x⟩
ds =
πp/2
‖s‖
p+2α
Γ(1 − α)
α2 2α Γ(α + 1 2 p) ‖x‖2α ,
with absolute convergence for all x. We shall describe
generalizations of this singular integral arising in the
theory of spherical functions on symmetric cones.
second derivative is only continuous in very rigid situations
that have a simple geometric description. The proof
weaves together analysis and geometry. For more, see my
article with Bill Minicozzi, “Level Set Method: For Motion
by Mean Curvature,” in the November 2016 issue of the
Notices.
(See www.ams.org/journals/notices/201610/
rnoti-p1148.pdf).
References
[1] J. Dueck, D. Edelmann, and D. Richards, Distance
correlation coefficients for Lancaster distributions, (2016),
http://arxiv.org/abs/1502.01413.
[2] M. T. Richards, D. St. P. Richards, and E. Martínez-Gómez,
Interpreting the distance correlation results for the COMBO-17
survey, Astrophys. J. Lett. 784:L34 (2014) (5 pp.).
[3] G. J. Székely, M. L. Rizzo, and N. K. Bakirov, Measuring and
testing independence by correlation of distances. Ann. Statist.
35 (2007), 2769–2794. MR2382665
[4] E. Volokh, Zero correlation between state homicide rate and
state gun laws. The Washington Post, October 6, 2015.
Tobias Holck Colding
Arrival Time
Modeling of a wide
range of physical
phenomena
leads to tracking
fronts moving
with curvaturedependent
speed.
A particularly natural
example is
where the speed is
the mean curvature.
If the movement
is monotone inwards,
then the
arrival time function
Tobias Holck Colding
is the time
when the front arrives
at a given point. It has long been known that
this function satisfies a natural differential equation
in a weak sense, but one wonders what is
the regularity. It turns out that one can completely answer
this question. It is always twice differentiable, and the
Figure 1. Droplets and crystal growth can be
modeled as moving fronts.
Figure 2. Cross-sections of a dumbbell moving by
mean curvature. Curves are level sets of the arrival
time function.
Tobias Holck Colding is Cecil and Ida B. Green Distinguished
Professor of Mathematics at MIT. His e-mail address is colding@
math.mit.edu.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1462
Figure 3. Kohn and Serfaty have given a game
theoretic interpretation of arrival time.
18 Notices of the AMS Volume 64, Number 1

Wilfrid Gangbo
Paths of Minimal Lengths on the Set of Exact
k-forms
Let Ω ⊂ R n be a bounded contractible
domain with smooth
boundary ∂Ω. The (linear)
Hodge decomposition of vector
fields states that any
smooth vector field v of Ω
into R n can be decomposed
into
(1) v = ∇φ 0 + v 0 ,
where v 0 is a differentiable
divergence-free vector field,
parallel to ∂Ω, and φ 0 ∶ Ω → R
is a differentiable function.
A very influential paper by
Y. Brenier revealed that any
Wilfrid Gangbo
square integrable vector field
satisfying a certain nondegeneracy
condition is, up to a change of variables that
preserves Lebesgue measure, the gradient of a realvalued
function. This remarkable result, termed “the
polar factorization of a vector field,” led to the mathematical
renaissance of the Monge-Kantorovich theory, now
called “optimal mass transportation theory.”
Since vector fields can be identified with differential
1-forms, roughly speaking, the polar factorization states
that any differential 1-form is exact up to a change of
coordinates that preserves Lebesgue measure. A natural
mathematical question is whether there exists an
analogous result for differential k-forms.
It is now time to justify why the polar factorization of a
vector field can be interpreted as a nonlinear Hodge factorization
and motivate the optimal transport of differential
forms.
Synopsis: Renaissance of the Monge-Kantorovich
Theory
Any vector field u ∶ Ω → R n transports any measure on Ω
to another measure on R n . For instance, the transport of
μ 0 , Lebesgue measure on Ω, produces the measure μ 1 on
R n defined by
μ 1 (B) ∶= μ 0 (u −1 (B))
for any B ⊂ R n . If u is nondegenerate, then μ 1 must be
absolutely continuous with respect to Lebesgue measure
Wilfrid Gangbo is professor of mathematics at UCLA. His e-mail
address is wgangbo@math.ucla.edu.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1458
on R n . In fact, by definition, u is nondegenerate means
that μ 1 vanishes on any (n − 1)-rectifiable set.
Assume without loss of generality that μ 0 (Ω) = 1, μ 0
represents the distribution of a fluid occupying Ω at time
t = 0, and μ 1 represents the distribution at time t = 1. The
fluid consists of infinitely many particles evolving over
time. Assume that at time t the velocity of the particle
located at x ∈ R n is v(t, ⋅) =∶ v t (x). At each time t, the
positions of the particles are represented by a probability
measure σ t . The total kinetic energy of the system at time
t is then
||v t || 2 L 2 (σ t) ∶= ∫ R n |v t (x)| 2 σ t (dx).
Formally, one views the set of probability measures
of bounded second moment as a manifold M. The
tangent space to M at σ ∈ M includes vector fields
v ∈ C ∞ c (R n , R n ). The metric at σ is such that ⟨v; v⟩ =
||v|| 2 L 2 (σ) .
The square Wasserstein distance between μ 0 and μ 1
is the minimal kinetic energy required by the fluid to
evolve from its initial to its final configuration. By a
reparametrization argument, the Wasserstein distance
between μ 0 and μ 1 is
(2)
W 2 (μ 0 , μ 1 )
∶= min
(σ,v){∫ 1 ||v t || L2 (σ t)dt | ∂ t σ + ∇ ⋅ (σv) = 0,
0
σ 0 = μ 0 , σ 1 = μ 1 }.
Here, the minimum is performed over the set of paths
t → (σ t , v t ) satisfying some measurability conditions for
the expression in (2) to make sense.
There exists a Lipschitz convex function ψ ∶ R d → R
such that the optimal σ is given by
(3)
σ t (B) = μ 1 ({y ∈ R n | ty+(1−t)∇ψ(y) ∈ B}), ∀ t ∈ [0, 1].
When t = 0, (3) means that S ∶= ∇ψ ∘ u preserves μ 0 .
Applying ∇φ to both sides of the identity S = ∇ψ ∘ u
with φ the Legendre transform of ψ, we have
(4) u = ∇φ ∘ S.
The pair (∇φ, S) is uniquely determined in (4). Pick any
v ∈ C ∞ (Ω) and apply the previous factorization to obtain
(5) id + εv = ∇φ ε ∘ S ε .
The uniqueness of the pair (∇φ ε , S ε ) yields for ε = 0 that
both ∇φ 0 and S 0 are the identity map. Thus,
(6) S ε = id + εv 0 + o(ε), ∇φ ε = id + ε∇φ 0 + o(ε).
Observe that for S ε to preserve Lebesgue measure for
every ε small enough, v 0 must be a divergence-free vector.
Combining (5) and (6), one concludes that
id + εv = id + ε(∇φ 0 + v 0 ) + o(ε),
and so the decomposition (1) holds.
January 2017 Notices of the AMS 19

There is another characterization of the map S in (4). It
is the unique minimizer of
(7) {||u − S|| L2 (μ 0) | S # μ 0 = μ 0 }.
In summary, the geodesic problem (2), the projection
problem (7), and the nonlinear factorization of vector
fields are all linked.
An Open Problem
An outstanding open problem is to know if we can
invent an optimal transport of k-forms, linked to a
nonlinear factorization of differential forms, that yields
the classical Hodge decomposition of differential k-forms
by a linearization procedure as above. Unfortunately, we
need to introduce some notation to state a meaningful
result. For instance, assume n = 2m and u ∈ C 1 (Ω) is
one-to-one. Let
m
ω m = ∑ dx i ∧ dx i+m
i=1
and consider the maps S ∶ Ω → Ω that pull ω m back to
itself; in other words,
(8)
m
∑
i=1
For any minimizer S of
dS i ∧ dS i+m = ∑ dx i ∧ dx i+m .
(9) {||u − S|| L2 (μ 0) | S satisfies (8), S ∈ Diff 1 (Ω, u(Ω))},
m
i=1
there exists a closed 2-form Φ such that
u = (δΦ ⌋ ω m ) ∘ S, dΦ = 0, and ∇ (δΦ ⌋ ω m ) ≥ 0.
Here, ⌋ is the interior product operator, and the interior
derivative δ is defined as minus the adjoint of the
exterior derivative operator d. In an ongoing collaborative
research program with B. Dacorogna and O. Kneuss, we
study extensions and variants of the projection problem
(9) and search for geodesics of minimal length.
Ingrid Daubechies
Reunited: Francescuccio Ghissi’s St. John
Altarpiece
Over a century ago, a
fourteenth-century altarpiece
was removed
from its church in
the Marche region in
Italy and dismantled.
The nine individual
scenes—eight smaller
pictures featuring St.
John the Evangelist
flanking a larger central
crucifixion—had
been sawn apart; the
resulting panels ended
up in different collections.
In the process,
the last of the eight
smaller scenes was
lost.
In preparation for
Ingrid Daubechies
an exhibition that
opened on September
10, 2016, the North Carolina Museum of Art (NCMA)
commissioned Dutch artist and art reconstruction expert
Charlotte Caspers to paint a replacement panel. Together
with NCMA curator David Steel, she designed a composition
in Ghissi’s style; the subject of the scene could be
determined from the Golden Legend, a medieval bestseller
chronicling lives of saints that was the source for the first
seven small panels.
The new panel demonstrated how bright and sparkling
these altarpieces were in their own time. But it became
Ingrid Daubechies is James B. Duke Professor of Mathematics
and Electrical and Computer Engineering at Duke University. Her
e-mail address is ingrid@math.duke.edu.
DOI: http://dx.doi.org/10.1090/noti1460
Figure 1a. The reunited altarpiece at the exhibition
comprises all of the old panels, in their present
condition, together with the aged version of panel 9.
Figure 1b. All of the rejuvenated panels of the St.
John Altarpiece by Francescuccio Ghissi, together
with Caspers’s panel 9.
20 Notices of the AMS Volume 64, Number 1

Figure 3. A “crack map” (right) for a detail of panel 3
(left).
Figure 2a. Panel 1, The Resurrection of Drusiana,
shown here in its present physical condition.
Figure 2b. With cracks removed and colors remapped,
the painted portion of The Resurrection of Drusiana
is rejuvenated.
clear that the new Caspers panel could not simply be
displayed next to the eight other panels in the same frame:
vivid and bright, it would lure the viewer’s attention away
from the faded originals, even though it was an imposter
next to the real panels.
The Duke IPAI (Image Processing for Art Investigation)
group, however, could help with this. By studying the old
as well as the new panels, we could “virtually age” the
new panel, i.e., make a digital copy in which the gold
would look duller, the colors would be altered to mimic
650 years of aging of the pigments, small cracks would
be added. A printout could then “complete” the reunited
Ghissi Altarpiece (as in Figure 1a) without distracting
from its authentic siblings.
The same technical
analysis can also
be applied in the reverse
direction. From
the correspondence
between “old” and
“new” for each pigment
mixture used in the
altarpiece, and after
fine-tuning the digital
The whole project
was really a
triumph of “how
math can help”
image manipulations to make the transition from new
to old, we can also take a high-resolution image of the
old panels and map their old, aged colors to corresponding
“freshly painted” versions, thus rejuvenating
the fourteenth-century panels (see Figure 2a and 2b).
The exhibition at NCMA features a printout of the
virtually aged panel, completing the others in a reunited
altarpiece, and showcases the bright new panel separately,
with a documentary on its painting process. It also shows
“old” and “new” versions of all panels and short videos
on the different image-processing and analysis steps that
made the reconstruction possible. Some of the image
processing we did was fairly standard and could be
carried out by means of programs like GIMP or Photoshop.
Other steps—such as automatically identifying
cracks (see Figure 3) so they could then be inpainted
or removing cradling artifacts from X-ray images of
the paintings—involved the development of new or very
recently developed approaches.
For instance, graduate student Rachel (Rujie) Yin first
carried out a nifty combination of a 2D Radon transform
with a wavelet transform in order to locate cradle artifacts
January 2017 Notices of the AMS 21

and then later used new machine-learning techniques
based on sparse expansions and dictionary identification,
which themselves emerged only in the last decade, to
remove from the X-ray images the woodgrain stemming
from the early twentieth-century cradle supports while
leaving intact the woodgrain from the original panels.
Since even the more established image-processing tools
we used are also based on very nice mathematical analysis,
the whole project was really a triumph of “how math can
help.” In fact, we now have several more projects with
the NCMA conservation and curatorial staff. When they
suggest a new collaboration, they preface it with, “We
wonder, could math help us with the following?”
For more information, see dukeipai.org/projects/
ghissi and ncartmuseum.org/exhibitions/view/
13698.
Daubechies: Photo of Ingrid Daubechies is courtesy of
Ingrid Daubechies.
Figure 1a is courtesy of Portland Art
Museum, NCMA, Metropolitan Museum in
NYC, and the Art Institute in Chicago.
Figure 1b is courtesy of IPAI group, Duke
University, and museums listed in Figure 1a.
Figure 2a is courtesy of Portland Art Museum.
Figure 2b is courtesy of IPAI group,
Duke University, and Portland Art Museum.
Figure 3 is courtesy of North Carolina
Museum of Art and IPAI group, Duke University;
and North Carolina Museum of Art.
Photo Credits
Simon: Photo of Barry Simon is courtesy of the California
Institute of Technology/Bob Paz.
Silverberg: Photos of Alice Silverberg, mathematicians
and cryptographers at the conference are courtesy of
Alice Silverberg.
Illustration from Alice’s Adventures in Wonderland
is in the public domain.
Jeffrey: Photo of Lisa Jeffrey is courtesy of Radford Neal.
Staffilani: Photo of Gigliola Staffilani is courtesy of Brye
Vickmark.
Figure 1 (source: https://commons.
wikimedia.org/wiki/File:Prismrainbow.svg).
Figure 2 (public domain: https://commons.
wikimedia.org/wiki/File:Rainbow10_-_
NOAA.jpg).
Wienhard: Photos of Anna Wienhard are courtesy of
Heidelberg Institute for Theoretical Studies.
Figures 1, 2, and 3 are by Jos Leys—www.
josleys.com.
Richards: Photo of Donald St. P. Richards is courtesy of
the University of Heidelberg.
Colding: Photo of Tobias Holck Colding is courtesy of
Bryce Vickmark/MIT.
Figure 1 was created by Matthew Kuo and
Christian Clasen (https://www.flickr.
com/photos/cambridgeuniversityengineering/5957374384/in/
photostream/.
Figure 2 is courtesy of James A. Sethian.
Figure 3 is courtesy of R. V. Kohn.
Gangbo: Photo of Wilfrid Gangbo is courtesy of Wilfrid
Gangbo.
22 Notices of the AMS Volume 64, Number 1

Barry Simon was born in Brooklyn, NY in 1946, graduated from Harvard in 1966, got a PhD in Physics from Princeton
in 1970 and tenure at Princeton jointly in Mathematics and Physics in 1972. Since 1981, he has been at Caltech where
he is currently the IBM Professor of Mathematics and Theoretical Physics emeritus. He is the author of 21 mathematics
books including the four volume Methods of Modern Mathematical Physics with Mike Reed and the recent five volume
Comprehensive Course in Analysis. He has over 63,000 citations and h-index of 105 on Google Scholar. His research
has included work in mathematical physics (including Schrödinger Operators, Constructive Quantum Field Theory, and
Statistical Mechanics) and in the spectral theory of orthogonal polynomials. His honors include a Putnam top five finish,
the Poincare Prize of the IAMP, and the AMS’ Steele Prize for Lifetime Achievement. He was on the cover of the August,
2016 Notices (see http://www.ams.org/publications/journals/notices/201607/noti-aug-16-cov-web.pdf).
Simon graduated from James Madison High School, a non-honors local Brooklyn school, but he is far from its most
distinguished alumnus. Other alumni include Ruth Bader Ginsburg, Chuck Schummer, and Bernie Sanders, as well
as four Nobel Laureates. His greatest influence there was Sam Marantz, a physics teacher who told him high school
physics was a waste of time and he should take the advanced placement course where Mr. Marantz gave him the version
of the book using calculus. It is the influence of Mr. Marantz that led Simon to study physics and had him apply to
and attend Harvard rather than Caltech where he intended to go until Mr. Marantz said he should go to Harvard.
Alice Silverberg’s early influences include two wonderful programs for young people, and the amazing individuals
who created and ran them. The first was the Children’s Center for the Creative Arts, which nurtured the creativity of
many children under the leadership of Grace Stanistreet, on Saturdays at Adelphi University. The second was Arnold
Ross’s summer program for high school students (and college-aged counselors) at Ohio State and the University of
Chicago. She also competed in the New York City math meets, and was captain of her high school’s Math Team.
Silverberg’s degrees are from Harvard, Cambridge, and Princeton, where she learned what it’s like to be a woman
at institutions that to a great extent still thought of themselves as men’s schools. After many years on the faculty at
Ohio State, Silverberg decided that she needed better weather and beaches, and moved in 2004 to the University of
California, Irvine.
Her mathematical interests started out mostly in number theory, and expanded to include the mathematics of
cryptography. Some of her current projects involve bringing together disparate communities (such as mathematicians
and cryptographers) to solve problems of common interest.
Lisa Jeffrey moved to northern Norway at age nine and was put in a math class two years above her age level. There,
Grade 6 students were taught ruler-and-compass constructions and Euclidean geometry. She got top marks on the
county-wide grade 6 exam, despite her young age and the language in which the exam was written—Norwegian, which
she had learned just six months earlier. She is grateful to her sixth-grade math teacher, Mr. Sæboe from Tromsdal
School, who nurtured and inspired her.
Later she was a physics major at Princeton University and did a DPhil in mathematics at Oxford University under the
supervision of Michael Atiyah. Jeffrey’s first postdoctoral fellowship was at IAS (Princeton, NJ) under the supervision
of Edward Witten.
She tells Notices that she owes debts of gratitude to her first research collaborators Frances Kirwan and Jonathan
Weitsman, with whom she began writing papers more than twenty years ago.
Gigliola Staffilani grew up on a farm in Martinsicuro, central Italy. She had no books until her older brother brought
some back from his school. Her father died when she was ten, and her mother decided then that Staffilani did not need
to continue on to high school. Fortunately, her brother helped her to change her mother’s mind.
At school Staffilani came to love mathematics and was encouraged by her teachers and her brother to continue
with those studies. She won a fellowship and arrived in Chicago for graduate school without speaking practically any
English and with the wrong type of visa for her fellowship (not having taken the TOEFL exam). This caused several
problems, among them not receiving her first fellowship stipend. Paul Sally intervened and loaned her enough money
to get by for that first month in the US.
While in Chicago Staffilani worked under the supervision of Carlos Kenig, and later she was mentored by Jean
Bourgain at the Institute for Advanced Study in Princeton before moving to Stanford University. It was around this
time that she started her most fruitful collaboration to date, with Jim Colliander, Markus Keel, Hideo Takaoka, and
Terry Tao, a group that is now referred to as the I-team. Staffilani is currently the Abby Rockefeller Mauze Professor of
Mathematics at the Massachusetts Institute of Technology. She lives in Cambridge, MA, with her husband and teenage
twins.
January 2017 Notices of the AMS 23

Anna Wienhard, after studying mathematics and protestant theology, received her PhD in mathematics from the
University of Bonn in 2004. She has been a postdoc at the University of Basel, the Institute for Advanced Study
Princeton, and the University of Chicago, and an assistant professor at Princeton University from 2007–2012. In 2012
she joined Heidelberg University in Germany as a full professor. Since 2015 she is also leading a research group at the
Heidelberg Institute for Theoretical Studies. She was a member of the Young National Academy of Sciences in Germany
from 2008–2013 and is a Fellow of the AMS since 2013.
From the beginning Wienhard’s mathematical tastes and choices were driven by the quest to find and reveal (hidden)
structures. Trained as a differential geometer, she became fascinated by symmetric spaces, and has since worked on the
interplay of discrete subgroups of Lie groups, homogeneous spaces, and deformation spaces of geometric structures.
Donald St. P. Richards’ interest in mathematics began at age nine when his mother showed him her copy of Elementary
Algebra for Schools, by Hall and Knight. With his mother’s help, Richards worked that summer and the next through the
first few chapters of Elementary Algebra. Continuing under the tutelage of a stream of superb mathematics teachers
in high school and in college, Richards went on to complete his PhD degree in 1978 under the direction of Rameshwar
Gupta at the University of the West Indies. Richards, a Fellow of the Institute of Mathematical Statistics and a Fellow of
the American Mathematical Society, is currently a Professor of Statistics at Penn State University.
Tobias Holck Colding completed his PhD under Christopher Croke at the University of Pennsylvania in 1992. Prior to
joining the Massachusetts Institute of Technology, he was professor at New York University’s Courant Institute. Colding
is a foreign member of the Royal Danish Academy of Science and Letters and Fellow of the American Academy of Arts
& Sciences. He received the 2010 Oswald Veblen Prize in Geometry and the 2016 Carlsberg Foundation Research Prize.
Wilfrid Gangbo’s primary and secondary research interests are Nonlinear Analysis, Calculus of Variations, Partial
Differential Equations and Fluid Mechanics, and Geophysics and Kinetic Theory, respectively. He has his PhD in applied
mathematics from Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland, 1992, and did his dissertation at
Université de Metz, France, 1995. Gangbo is currently Professor of Mathematics at UCLA and Professor of Mathematics
at he School of Mathematics, Georgia Tech.
Throughout his career he has had the pleasure of supervising PhD students M. Agueh (2002), H. Maroofi (2002), T.
Yolcu (2009), H.-K. Kim (2009), M. Sedjro (2012), R. Awi (2015), and S. Mayorga (currently).
International outreach is of great importance to Gangbo; he is founder of EcoAfrica, an association of scientists
involved in projects in support of African countries. EcoAfrica was founded in Switzerland in 1990 and currently has
six members. Among other activities, EcoAfrica has organized several workshops in Applied Mathematics in Senegal
and intends to do the same in other countries in Africa. Gangbo is also a member of the advisory board of the African
Center for Excellence in Mathematics and Applications. Located in the Republic of Benin, West Africa, the Center’s
mission includes the training of graduate students and the organization of scientific activities, to raise the quality of
human resources in Benin and neighboring countries.
Ingrid Daubechies’ research interests are time-frequency analysis (in particular but by no means exclusively, wavelets)
and applications to mathematics, to the other sciences, to engineering, and to art. Daubechies received her Bachelors
degree in Physics and her PhD in Theoretical Physics from Vrije Universiteit Brussel. According to Daubechies, she has
no degree in mathematics and only pretends at being a mathematician.
Daubechies was born in Belgium and became a naturalized US citizen in 1996. She is the James B. Duke Professor of
Mathematics and Electrical and Computer Engineering at Duke University. Throughout her career Daubechies has been
the recipient of many honors and awards; she is thrilled to be the recipient of the Simons Investigators 2016 Award in
Math+X.
She is most known for her work constructing the first examples of what mathematicians call “wavelets,” which have
had an immense impact on pure and applied mathematics. Daubechies has been fascinated for as long as she can
remember with how things work and how you can make them work if they don’t at first. She continues to make creative
applications of wavelets and other analysis tools to a large variety of problems in engineering and other fields.
24 Notices of the AMS Volume 64, Number 1

Editor’s Note: Matt Baker is speaking on this topic in the Current Events Bulletin Lecture at the January 2017 Joint
Mathematics Meetings.
Karim Adiprasito, June Huh, and Eric Katz
Communicated by Benjamin Braun
Introduction
Logarithmic concavity is a property of a sequence of
real numbers, occurring throughout algebraic geometry,
convex geometry, and combinatorics. A sequence of
positive numbers a 0 , … , a d is log-concave if
a 2 i ≥ a i−1 a i+1 for all i.
This means that the logarithms, log(a i ), form a concave
sequence. The condition implies unimodality of the sequence
(a i ), a property easier to visualize: the sequence
is unimodal if there is an index i such that
a 0 ≤ ⋯ ≤ a i−1 ≤ a i ≥ a i+1 ≥ ⋯ ≥ a d .
We will discuss our work on establishing log-concavity
of various combinatorial sequences, such as the coefficients
of the chromatic polynomial of graphs and the
face numbers of matroid complexes. Our method is motivated
by complex algebraic geometry, in particular Hodge
theory. From a given combinatorial object M (a matroid),
we construct a graded commutative algebra over the real
numbers
A ∗ (M) =
d
⨁
q=0
A q (M),
Karim Adiprasito is assistant professor of mathematics at Hebrew
University of Jerusalem. His e-mail address is adiprasito@math.
huji.ac.il.
June Huh is research fellow at the Clay Mathematics Institute and
Veblen Fellow at Princeton University and the Institute for Advanced
Study. His e-mail is huh@princeton.edu.
Eric Katz is assistant professor of mathematics at the Ohio State
University. His e-mail address is katz.60@osu.edu.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1463
which satisfies analogues of Poincaré duality, the hard Lefschetz
theorem, and the Hodge-Riemann relations for the
cohomology of smooth projective varieties. Log-concavity
will be deduced from the Hodge-Riemann relations for
M. We believe that behind any log-concave sequence
that appears in nature there is such a “Hodge structure”
responsible for the log-concavity.
Coloring Graphs
Generalizing earlier work of George Birkhoff, in 1932
Hassler Whitney introduced the chromatic polynomial of
a connected graph G as the function on N defined by
χ G (q) = |{proper colorings of G using q colors}|.
In other words, χ G (q) is the number of ways to color
the vertices of G using q colors so that the endpoints of
every edge have different colors. Whitney noticed that the
chromatic polynomial is indeed a polynomial. In fact, we
can write
χ G (q)/q = a 0 (G)q d − a 1 (G)q d−1 + ⋯ + (−1) d a d (G)
for some positive integers a 0 (G), … , a d (G), where d is
one less than the number of vertices of G.
Example 1. The square graph
• •
• •
has the chromatic polynomial 1q 4 − 4q 3 + 6q 2 − 3q.
The chromatic polynomial was originally devised as
a tool for attacking the Four Color Problem, but soon
it attracted attention in its own right. Ronald Read
conjectured in 1968 that the coefficients of the chromatic
polynomial form a unimodal sequence for any graph.
26 Notices of the AMS Volume 64, Number 1

A few years later, Stuart Hoggar conjectured that the
coefficients in fact form a log-concave sequence:
a i (G) 2 ≥ a i−1 (G)a i+1 (G) for any i and G.
The graph theorist William Tutte quipped, “In compensation
for its failure to settle the Four Colour Conjecture, [the
chromatic polynomial] offers us the Unimodal Conjecture
for our further bafflement.”
The chromatic polynomial can be computed using the
deletion-contraction relation: if G\e is the deletion of an
edge e from G and G/e is the contraction of the same
edge, then
χ G (q) = χ G\e (q) − χ G/e (q).
The first term counts the proper colorings of G, the
second term counts the otherwise-proper colorings of G
where the endpoints of e are permitted to have the same
color, and the third term counts the otherwise-proper
colorings of G where the endpoints of e are mandated to
have the same color. Note that, in general, the sum of two
log-concave sequences is not a log-concave sequence.
Example 2. To compute the chromatic polynomial of the
square graph above, we write
and use
• •
• •
=
• •
• •
-
• ❅ ❅
• •
χ G\e (q) = q(q − 1) 3 , χ G/e (q) = q(q − 1)(q − 2).
The Hodge-Riemann relations for the algebra A ∗ (M),
where M is the matroid attached to G as in the section
“Matroids” below, imply that the coefficients of the
chromatic polynomial of G form a log-concave sequence.
This is in contrast to a result of Alan Sokal that the set of
roots of the chromatic polynomials of all graphs is dense
in the complex plane.
Counting Independent Subsets
Linear independence is a fundamental notion in algebra
and geometry: a collection of vectors is linearly independent
if no nontrivial linear combination sums to zero.
How many linearly independent collections of i vectors
are there in a given configuration of vectors? Write A for
a finite subset of a vector space and f i (A) for the number
of independent subsets of A of size i.
Example 3. If A is the set of all nonzero vectors in the
three-dimensional vector space over the field with two
elements, then
f 0 = 1, f 1 = 7, f 2 = 21, f 3 = 28.
Examples suggest a pattern leading to a conjecture of
Dominic Welsh:
f i (A) 2 ≥ f i−1 (A)f i+1 (A) for any i and A.
For any small specific case, the conjecture can be verified
by computing the f i (A)’s by the deletion-contraction relation:
if A\v is the deletion of a nonzero vector v from A
and A/v is the projection of A in the direction of v, then
f i (A) = f i (A\v) + f i−1 (A/v).
The first term counts the number of independent subsets
of size i, the second term counts the independent subsets
of size i not containing v, and the third term counts
the independent subsets of size i containing v. As in
the case of graphs, we notice the apparent interference
between the log-concavity conjecture and the additive
nature of f i (A). The sum of two log-concave sequences is,
in general, not log-concave. The conjecture suggests a new
description for the numbers f i (A) and a corresponding
structure of A.
Matroids
In the 1930s Hassler Whitney observed that several
notions in graph theory and linear algebra fit together in
a common framework, that of matroids. This observation
started a new subject with applications to a wide range
of topics such as characteristic classes, optimization, and
moduli spaces, to name a few.
Let E be a finite set. A matroid M on E is a collection
of subsets of E, called flats of M, satisfying the following
axioms:
(1) If F 1 and F 2 are flats of M, then their intersection is
a flat of M.
(2) If F is a flat of M, then any element of E\F is
contained in exactly one flat of M covering F.
(3) The ground set E is a flat of M.
Here, a flat of M is said to cover F if it is minimal among
the flats of M properly containing F. For our purposes,
we may assume that M is loopless:
(1) The empty subset of E is a flat of M.
Every maximal chain of flats of M has the same length,
and this common length
is called the rank of
M. We write M\e for
the matroid obtained
by deleting e from the
flats of M and M/e for
the matroid obtained by
deleting e from the flats
of M containing e. When
M 1 is a matroid on E 1 ,
M 2 is a matroid on E 2 ,
Matroids encode
a combinatorial
structure
common to
graphs and
vector
configurations
and E 1 ∩ E 2 is empty,
the direct sum M 1 ⊕ M 2
is defined to be the matroid
on E 1 ∪ E 2 whose
flats are all sets of the
form F 1 ∪ F 2 , where F 1 is a flat of M 1 and F 2 is a flat of M 2 .
Matroids encode a combinatorial structure common to
graphs and vector configurations. If E is the set of edges
of a finite graph G, call a subset F of E a flat when there is
no edge in E\F whose endpoints are connected by a path
in F. This defines a graphic matroid on E. If E is a finite
subset of a vector space, call a subset F of E a flat when
there is no vector in E\F that is contained in the linear
span of F. This defines a linear matroid on E.
January 2017 Notices of the AMS 27

Example 4. Write E = {0, 1, 2, 3} for the set of edges of
the square graph G in Example 1. The graphic matroid M
on E attached to G has flats
∅, {0}, {1}, {2}, {3}, {0, 1}, {0, 2}, {0, 3},
{1, 2}, {1, 3}, {2, 3}, {0, 1, 2, 3}.
Example 5. Write E = {0, 1, 2, 3, 4, 5, 6} for the configuration
of vectors A in Example 3. The linear matroid M on
E attached to A has flats
∅, {0}, {1}, {2}, {3}, {4}, {5}, {6},
{1, 2, 3}, {3, 4, 5}, {1, 5, 6}, {0, 1, 4}, {0, 2, 5}, {0, 3, 6},
{2, 4, 6}, {0, 1, 2, 3, 4, 5, 6}.
A linear matroid that arises from a subset of a vector
space over a field k is said to be realizable over k.
Not surprisingly, this notion is sensitive to the field k.
A matroid may arise from a vector configuration over
one field, while no such vector configuration exists over
another field. Many matroids are not realizable over any
field.
Among the rank 3 loopless matroids pictured above,
where rank 1 flats are represented by points and rank
2 flats containing more than two points are represented
by lines, the first is realizable over k if and only if the
characteristic of k is 2, the second is realizable over k if
and only if the characteristic of k is not 2, and the third
is not realizable over any field.
The characteristic polynomial χ M (q) of a matroid M is
a generalization of the chromatic polynomial χ G (q) of a
graph G. It can be recursively defined using the following
rules:
(1) If M is the direct sum M 1 ⊕ M 2 , then
χ M (q) = χ M1 (q) χ M2 (q).
(2) If M is not a direct sum, then, for any e,
χ M (q) = χ M\e (q) − χ M/e (q).
(3) If M is the rank 1 matroid on {e}, then
χ M (q) = q − 1.
(4) If M is the rank 0 matroid on {e}, then
χ M (q) = 0.
It is a consequence of the Möbius inversion for partially
ordered sets that the characteristic polynomial of M is
well defined.
We may now state our result in [AHK], which confirms
a conjecture of Gian-Carlo Rota and Dominic Welsh.
Theorem 6 ([AHK, Theorem 9.9]). The coefficients of the
characteristic polynomial form a log-concave sequence
for any matroid M.
This implies the log-concavity of the sequence a i (G)
[Huh12] and the log-concavity of the sequence f i (A)
[Len12].
Hodge-Riemann Relations for Matroids
Let X be a mathematical object of “dimension” d. Often it
is possible to construct from X in a natural way a graded
vector space over the real numbers
A ∗ (X) =
d
⨁
q=0
A q (X),
equipped with a graded bilinear pairing
and a graded linear map
P ∶ A ∗ (X) × A d−∗ (X) ⟶ R,
L ∶ A ∗ (X) ⟶ A ∗+1 (X),
x ⟼ Lx
(“P” is for Poincaré, and “L” is for Lefschetz). For example,
A ∗ (X) may be the cohomology of real (p, p)-forms on a
compact Kähler manifold X or the ring of algebraic cycles
modulo homological equivalence on a smooth projective
variety X or the combinatorial intersection cohomology
of a convex polytope X [Kar04] or the Soergel bimodule
of an element of a Coxeter group X [EW14] or the Chow
ring of a matroid X defined below. We expect that, for
every nonnegative integer q ≤ d 2 :
(1) the bilinear pairing
P ∶ A q (X) × A d−q (X) ⟶ R
is nondegenerate (Poincaré duality for X),
(2) the composition of linear maps
L d−2q ∶ A q (X) ⟶ A d−q (X)
is bijective (the hard Lefschetz theorem for X), and
(3) the bilinear form on A q (X) defined by
(x 1 , x 2 ) ⟼ (−1) q P(x 1 , L d−2q x 2 )
is symmetric and is positive definite on the kernel
of
L d−2q+1 ∶ A q (X) ⟶ A d−q+1 (X)
(the Hodge-Riemann relations for X).
All three properties are known to hold for the objects listed
above except one, which is the subject of Grothendieck’s
standard conjectures on algebraic cycles.
For a loopless matroid M on E, the vector space A ∗ (M)
has the structure of a graded algebra that can be described
explicitly.
Definition 7. We introduce variables x F , one for each
nonempty proper flat F of M, and set
S ∗ (M) = R[x F ] F≠∅,F≠E .
The Chow ring A ∗ (M) of M is the quotient of S ∗ (M) by
the ideal generated by the linear forms
∑ x F − ∑ x F ,
i 1∈F i 2∈F
one for each pair of distinct elements i 1 and i 2 of E, and
the quadratic monomials
x F1 x F2 ,
one for each pair of incomparable nonempty proper flats
F 1 and F 2 of M.
28 Notices of the AMS Volume 64, Number 1

The Chow ring of M was introduced by Eva Maria
Feichtner and Sergey Yuzvinsky. When M is realizable
over a field k, it is the Chow ring of the “wonderful”
compactification of the complement of a hyperplane
arrangement defined over k as described by Corrado de
Concini and Claudio Procesi.
Let d be the integer one less than the rank of M.
Theorem 8 ([AHK, Proposition 5.10]). There is a linear
bijection
deg∶ A d (M) ⟶ R
uniquely determined by the property that
deg(x F1 x F2 ⋯ x Fd ) = 1
for every maximal chain of nonempty proper flats
F 1 ⊊ F 2 ⊊ ⋯ ⊊ F d .
In addition, the bilinear pairing
P ∶ A q (M) × A d−q (M) → R,
(x, y) ↦ deg(xy)
is nondegenerate for every nonnegative q ≤ d.
What should be the linear operator L for M? We collect
all valid choices of L in a nonempty open convex cone.
The cone is an analogue of the Kähler cone in complex
geometry.
Definition 9. A real-valued function c on 2 E is said to be
strictly submodular if
c ∅ = 0, c E = 0,
and, for any two incomparable subsets I 1 , I 2 ⊆ E,
c I1 + c I2 > c I1 ∩I 2
+ c I1 ∪I 2
.
A strictly submodular function c defines an element
L(c) = ∑ c F x F ∈ A 1 (M)
F
that acts as a linear operator by multiplication
A ∗ (M) ⟶ A ∗+1 (M),
x ⟼ L(c)x.
The set of all such elements is a convex cone in A 1 (M).
The main result of [AHK] states that the triple
(A ∗ (M), P, L(c)) satisfies the hard Lefschetz theorem
and the Hodge-Riemann relations for every strictly submodular
function c:
Theorem 10. Let q be a nonnegative integer less than d 2 .
(1) The multiplication by L(c) defines an isomorphism
A q (M) ⟶ A d−q (M),
x ⟼ L(c) d−2q x.
(2) The symmetric bilinear form on A q (M) defined by
(x 1 , x 2 ) ⟼ (−1) q P(x 1 , L(c) d−2q x 2 )
is positive definite on the kernel of L(c) d−2q+1 .
The known proofs of the hard Lefschetz theorem and
the Hodge-Riemann relations for the different types of
objects listed above have certain structural similarities,
but there is no known way of deducing one from the
others.
Sketch of Proof of Log-Concavity
We now explain why the Hodge-Riemann relations for
M imply log-concavity for χ M (q). The Hodge-Riemann
relations for M, in fact, imply that the sequence (m i ) in
the expression
χ M (q)/(q − 1) = m 0 q d − m 1 q d−1 + ⋯ + (−1) d m d
is log-concave, which is stronger.
We define two elements of A 1 (M): for any j ∈ E, set
α M = ∑ x F ,
j∈F
β M = ∑ x F .
j∉F
The two elements do not depend on the choice of j, and
they are limits of elements of the form L(c) for strictly
submodular c. A short combinatorial argument shows
that m i is a mixed degree of α M and β M :
m i = deg(α i M β d−i
M ).
Thus, it is enough to prove for every i that
deg(α d−i+1
M
β i−1
M
)deg(α d−i−1
M
β i+1
M
) ≤ deg(αM d−i β i M) 2 .
This is an analogue of the Teisser-Khovanskii inequality
for intersection numbers in algebraic geometry and
the Alexandrov-Fenchel inequality for mixed volumes in
convex geometry. The main case is when i = d − 1.
By a continuity argument, we may replace β M by
L = L(c) sufficiently close to β M . The desired inequality
in the main case then becomes
deg(α 2 ML d−2 )deg(L d ) ≤ deg(α M L d−1 ) 2 .
This follows from the fact that the signature of the bilinear
form
A 1 (M) × A 1 (M) → R, (x 1 , x 2 ) ↦ deg(x 1 L d−2 x 2 )
restricted to the span of α M and L is semi-indefinite,
which, in turn, is a consequence of the Hodge-Riemann
relations for M in the cases q = 0, 1.
This application uses only a small piece of the Hodge-
Riemann relations for M. The general Hodge-Riemann
relations for M may be used to extract other interesting
combinatorial information about M.
References
[AHK] Karim Adiprasito, June Huh, and Eric Katz, Hodge
theory for combinatorial geometries, arXiv:1511.02888.
[EW14] Elias-Williamson, Ben Elias, and Geordie
Williamson, The Hodge theory of Soergel bimodules,
Ann. Math. (2) 180 (2014), 1089–1136.
MR3245013
[Huh12] June Huh, Milnor numbers of projective hypersurfaces
and the chromatic polynomial of graphs, J. Amer. Math.
Soc. 25 (2012), 907–927. MR2904577
[Kar04] Kalle Karu, Hard Lefschetz theorem for nonrational
polytopes, Invent. Math. 157 (2004), 419–447.
MR2076929
[Len12] Matthias Lenz, The f-vector of a representablematroid
complex is log-concave, Adv. in Appl. Math. 51
(2013), no. 5, 543–545. MR3118543
January 2017 Notices of the AMS 29

Announcing...
The creators of MathJobs.Org welcome you to:
MathPrograms.Org
Photo Credits
Photo of June Huh is courtesy of Nayoung Kim.
Photo of Eric Katz is courtesy of Joseph Rabinoff.
THE AUTHORS
Karim Adiprasito
Receive, read, rate, and
respond to electronic
applications for your
mathematical sciences
programs, such as undergraduate summer
research programs and travel grant
competitions.
June Huh
Customize your settings and control the
application form; also set secure access for
the admissions committee.
Enter program announcements for public
display.
Eric Katz
Download data to personal computers for
use in word processing and spreadsheets or
as a full permanent storage file.
Service is FREE to applicants.
Institutions pay annually for
one program or for multiple
programs.
30 Notices of the AMS Volume 64, Number 1

AMERICAN MATHEMATICAL SOCIETY
The AMS Graduate Student Blog
Talk that matters to mathematicians.
From “Things You Should Do
Before Your Last Year”…
Write stuff up. Write up background,
write down little ideas and bits of
progress you make. It’s difficult to
imagine that these trivial, inconsequential
bits will make it to
your dissertation. But recreating a
week’s/ month’s worth of ideas is
way more time-consuming that just
writing them down
now. Or better yet,
TeX it up.
From “The Glory of Starting Over”…
What I would recommend is not being too
narrowly focused, but finding a few things
that really interest you and develop different
skillsets. Make sure you can do some things
that are abstract, but also quantitative/programming
oriented things, because this shows
that you can attack a problem from multiple
angles. In my experience, these two sides also
serve as nice vacations from each other, which
can be important when you start to work hard
on research.
From “Student Seminar”…
A talk can be too short if not enough material is introduced to make it
interesting, but in research level talks, the last third of the talk (approximately)
is usually very technical and usually only accessible to experts
in the field. I will avoid going into details that are not of general interest
and I plan to present more ideas than theorems. The
most important thing when giving any
talk is to know your audience.
AMS
Grad
Blog
Advice on careers, research, and going the
distance … by and for math grads.
mathgradblog.williams.edu/

THE GRADUATE STUDENT SECTION
Art hur Benjamin Interview
Arthur Benjamin is Smallwood Family Professor
of Mathematics at Harvey Mudd College. He coauthored
the award-winning book Proofs That
Really Count, and most recently he was awarded the
Joint Policy Board for Mathematics Communications
Award in 2016. He is also known for his
“Mathemagics” shows, where he demonstrates and
explains how to do rapid mental calculations. He has
given three TED talks, which have been viewed over
12 million times.
DOI: http://dx.doi.org/10.1090/noti1470
Diaz-Lopez: When did you know you wanted to be a mathematician?
Benjamin: That came pretty late for me. When I started
college I remember thinking I would not be a professor
because it would take about ten years of school and,
when you are eighteen, that
seems like a large fraction of
your life. But when you are
graduating you think, “Oh,
in another three to five years
I could have the credentials
to be a college professor.
Let’s do it.” Then I got my
first taste of being a TA in
graduate school, and I loved
it. I loved being in front of a
classroom, and I thought if I
get paid to teach and explain
math to other people, how
great would that be?
Diaz-Lopez: Who encouraged
or inspired you (mathematically
or otherwise)?
Benjamin: My favorite
professor in graduate school
was Ed Scheinerman in the
If you get
discouraged
on a
problem, let
it sit, put it
aside, and
work on
something
else
Department of Applied Mathematics and Statistics at
Johns Hopkins University. Ed is a fantastic teacher and
a wonderful human being. He has been a role model for
me professionally.
Diaz-Lopez: How would you describe your research to
a graduate student?
Benjamin: Most of the work I’ve done in the last twenty
years has been in the area of finding combinatorial proofs
for interesting mathematical identities. A lot of them have
to do with Fibonacci numbers and their generalizations,
continued fractions, and determinants. My PhD is not in
pure mathematics, so the work that I do has to be simple.
I’m at an institution where I work with talented undergraduates,
so it’s a nice fit.
Diaz-Lopez: What theorem are you most proud of and
what was the most important idea that led to this breakthrough?
Benjamin: “A Combinatorial Proof of Vandermonde’s
Determinant,” with Greg Dresden, published in the American
Mathematical Monthly in 2007. The proof consisted
of a card-counting argument. It involved sorting cards on
a table and counting the arrangements in various ways.
32 notices of the aMs VoluMe 64, nuMber 1

THE GRADUATE STUDENT SECTION
Diaz-Lopez: What advice do you have for graduate
students?
Benjamin: Don’t be afraid to change directions. I
switched graduate schools after my first year. I started
at Cornell’s Operations Research Department. It’s a great
department, but I didn’t have a strong enough pure
math background coming in, since I had concentrated
in statistics as an undergraduate (at Carnegie Mellon). I
didn’t know if I could manage the next four years with
the background I had. So I took a step back, went home,
then to Johns Hopkins, and started again. It was smoother
sailing after that. My experience having seen both graduate
programs has been very valuable for me in terms of the
contacts I made and the different approaches that I experienced.
It’s good for students to know that there are going
to be highs and lows during their graduate school career.
Diaz-Lopez: All mathematicians feel discouraged occasionally.
How do you deal with discouragement?
Benjamin: I recommend having lots of different problems
to work on. If you get discouraged on a problem, let it
sit, put it aside, and work on something else. More broadly,
I think it’s good to have lots of passions in your life, so
when math is not treating you well, then pay attention to
other things that you love to do.
Diaz-Lopez: You have won several honors and awards.
Which one has been the most meaningful and why?
Benjamin: The Joint Policy Board for Mathematics
(JPBM) Communications Award. I am honored and humbled
to be the newest recipient of this award. It has been
awarded to Martin Gardner, Ivars Peterson, Keith Devlin,
Nate Silver, Steve Strogatz, and others who have brought
mathematics to the masses. It has always been my goal to
get people excited about mathematics.
Diaz-Lopez: Apart from your mathematics, you are very
well known for your “Mathemagical” presentations. How
did you get involved in this?
Benjamin: As a kid I loved doing magic, and I grew up
in a very theatrical family. My father was an accountant
by day and an actor/director by night. My brother and
sister and I were all put on the stage at an early age. I’ve
always thought of myself as an entertainer. Even in the
classroom and in my writing, I want people to enjoy what
I am doing. I was fascinated with magic and did shows for
children throughout the east side of Cleveland, Ohio, as
“The Great Benjamini.” It was the traditional rabbit-outof-the-hat,
make-the-kids-laugh type of magic. As I started
doing shows for older audiences I moved into the area of
magic known as mentalism, which is magic of the mind.
My dad then suggested that I include some of my mental
math feats, which had always been a hobby of mine. I was
fascinated with numbers and finding new ways for multiplying
numbers, squaring, and so on. Much to my surprise,
the mental math part of my show got the best reaction.
Over the course of a couple of years that became the main
focus of my show. I stopped doing the “fake mind-reading
stuff” because I didn’t want to promote pseudoscience.
By focusing on mental math, I could teach my calculating
techniques to the audience, which they enjoyed a lot.
Diaz-Lopez: What’s the square of 283?
Arthur Benjamin in a mental math performance at the
Curiosity Retreat 2015 in Gateway, Colorado.
Benjamin: [In a fraction of a second] That would be
80,089.
Diaz-Lopez: While magicians usually do not reveal their
secrets, can you explain to us how you did that so quickly?
Benjamin: Absolutely. Let’s begin with a two-digit
square and then go up to three digits. Let’s start with the
square of 17. You may already know that the answer is
289, but here is how you would square it using my method.
I multiply 20 by 14 to get 280, then add the square of 3
to get 289. Algebraically, this is A 2 = (A + d)(A-d) + d 2 ,
where A = 17 and d = 3. Once you get comfortable squaring
two-digit numbers, you can attempt squaring three-digit
numbers. For the square of 283 I go up 17 to 300, down
17 to 266, and multiply 300 by 266 to get 79,800. Next I
add the square of 17 to get 79,800 + 289 = 80,089.
Diaz-Lopez: You have given almost 300 research
presentations, published almost 100 papers, refereed for
numerous journals, and published many books. Given
your many commitments, what techniques do you use to
manage your time?
Benjamin: I would be remiss if I didn’t mention my
fantastic wife, Deena, who has been incredibly supportive
throughout my career. I am also very fortunate to be in
a department that values my nontraditional activities, as
I give talks to colleges, universities, and student groups
around the world. They view that as a good thing, even
though it cuts into my traditional research productivity.
Early in my career I spent a lot of time preparing my
classes, so my research mainly got done during summers
and holidays. Eventually, I was able to do research during
the school year. Still, I was most productive during
the summer. After tenure, my research turned the corner
when I began a fruitful collaboration with Jennifer Quinn.
Diaz-Lopez: Any final comment or advice?
Benjamin: Professors in graduate school are likely to
encourage you to pursue an intense research career. They
want their students to become faculty members at PhDgranting
institutions, even though the reality is that the
vast majority of graduate students won’t end up there.
Don’t be afraid to strongly pursue other academic options.
I think teaching at a four-year college is a wonderful place
January 2017 Notices of the AMS 33

THE GRADUATE STUDENT SECTION
to be. I feel that it’s easier to enjoy your research at a
teaching-oriented institution than to enjoy your teaching
at a research-oriented institution. Harvey Mudd College
was a great fit for me, and I am very happy that I made
that choice for my career.
Editor’s Note: Benjamin’s latest book, The Magic of
Math, is featured in the “BookShelf” in this issue of the
Notices (See p. 50).
Photo Credit: Photo of performance is courtesy of
Harvey Mudd College.
You’re
Invited
The Editor-in-Chief invites all
readers, from students to retired
folks, to get more involved with
Notices as authors, editors, guest
editors, writers of Letters
to the Editor, and so on.
E-mail your interests, ideas, or
nominations of others to
Frank.Morgan@williams.edu.
Alexander Diaz-Lopez, having
earned his PhD at the University
of Notre Dame, is now visiting assistant
professor at Swarthmore
College. Diaz-Lopez was the first
graduate student member of the
Notices Editorial Board.
34 Notices of the AMS Volume 64, Number 1

a Complex Symmetric
Operator?
Stephan Ramon Garcia
Communicated by Steven J. Miller and Cesar E. Silva
What do these matrices have in common:
[ 0 1
0 0 ] , [1 2
3 4 ] , ⎡ 0 7 0
⎢0 1 5⎤⎥
, and ⎡ 9 8 9
⎢0 7 0⎤⎥
?
⎣0 0 6⎦
⎣0 0 7⎦
They each possess a well-hidden symmetry, for they are
unitarily similar to the symmetric, but non-Hermitian,
matrices
and
⎡
⎢
⎣
⎡
⎢
⎣
[ − 1 2
− i 2
− i 2
1
2
] ,
5−√34
2
⎡
−
2
i
⎣
− i 2
5+√34
2
⎤ ,
⎦
2 + √
57
2
0 − 1 2 i √ 37 − 73 √ 2 57
0 2 − √
57
2
− 1 2 i √ 37 + 73 √ 2 57
− 1 2 i √ 37 − 73 √ 2 57 − 1 2 i √ 37 + 73 √ 2 57 3
8 − √149
2
9
2
i √16837+64√149
√13093
i √133672−1296√149
√13093
9
2
i √16837+64√149
√13093
207440+9477√149
26186
18 √ 3978002+82324√149
13093
i √133672−1296√149
√13093
⎤
⎥
,
⎦
18 √ 3978002+82324√149
13093
92675+1808√149
13093
⎤
,
⎥
respectively. (n × n matrices A and B are unitarily similar
if A = U ∗ BU, where U is unitary and U ∗ is its adjoint;
operator theorists prefer the term unitarily equivalent
instead.) The existence of these hidden symmetries is
Stephan Ramon Garcia is associate professor of mathematics at
Pomona College. His e-mail address is Stephan.Garcia@pomona.
edu.
The author was partially supported by National Science Foundation
grant DMS-1265973.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1454
⎦
best explained in the framework of complex symmetric
operators, a surprisingly large class of tractable and
well-behaved operators.
Let H be a complex Hilbert space. Examples include
C n , the Lebesgue spaces L 2 (X, μ) of square-integrable
functions on X with respect to a measure μ, the spaces
l 2 (N) and l 2 (Z) of square integrable sequences indexed
by N and Z, and the Hardy Hilbert space H 2 of holomorphic
functions on the unit disk with square-summable Taylor
coefficients at the origin. A conjugate-linear, isometric,
involution C ∶ H → H is a conjugation on H; these are
the Hilbert space analogues of complex conjugation. An
example is [Cf](x) = f(1 − x) on L 2 [0, 1].
A linear operator T ∶ H → H is bounded if ‖T‖ ∶=
sup{‖Tx‖ ∶ ‖x‖ ≤ 1} is finite. A bounded linear operator
T ∶ H → H is C-symmetric if T = CT ∗ C; it is complex
symmetric if T is C-symmetric with respect to some
C. Unbounded examples appear in the complex scaling
theory for Schrödinger operators, certain non-self-adjoint
boundary value problems, and PT-symmetric quantum
theory [1].
What is the relationship between complex symmetric
operators and complex symmetric matrices? If C is a
conjugation on H, then there is an orthonormal basis
(e n ) of H whose elements are fixed by C: Ce n = e n
for all n. Since ⟨Cx, Cy⟩ = ⟨y, x⟩ for all x, y ∈ H, the
matrix of a C-symmetric operator T with respect to (e n )
is symmetric:
[T] i,j = ⟨Te j , e i ⟩ = ⟨CT ∗ Ce j , e i ⟩ = ⟨Ce i , T ∗ Ce j ⟩
= ⟨Te i , e j ⟩ = [T] j,i .
For example, T = CT ∗ C for
T = ⎡ 0 1 0
⎢0 0 1⎤⎥
⎣0 0 0⎦
and
z 1
z 2
z 3
z 2
C ⎡ ⎢ ⎤ ⎥ = ⎡ ⎢ ⎤ ⎥ .
⎣z 3 ⎦ ⎣z 1 ⎦
January 2017 Notices of the AMS 35

Form a unitary
U = ⎡ ⎢ ⎢⎢
⎣
1
2
− 1
√2
1
2
1
2
− i
√2
1
0
√2
1
2
i
√2
⎤
⎥
,
each of whose columns is fixed by C, and perform the
corresponding change of basis:
U ∗ TU = ⎡ ⎢
⎣
− 1
√2
0
1
√2
− i 2
⎦
0 −
2
i
i
2
⎤⎥ .
i
2
0
Voilá! A hidden symmetry is revealed! There are now
procedures to test for the existence of a compatible
conjugation; this is how some of the matrices above were
discovered.
This suggests a striking result: each square complex
matrix is similar to a complex symmetric matrix. Here is
the proof: every matrix is similar to its Jordan canonical
form, and every Jordan block is unitarily similar to a
complex symmetric matrix (mimic the example above).
Thus, A = A T reveals nothing about the Jordan structure
of A. On the other hand, A = A ∗ ensures that A has an
orthonormal basis of eigenvectors and only real eigenvalues.
How can this be? It takes 2(1 + 2 + ⋯ + n) = n 2 + n
real parameters to specify an n × n complex symmetric
matrix but only 2(1 + 2 + ⋯ + (n − 1)) + n = n 2 real
parameters to specify an n × n Hermitian matrix, since its
diagonal entries are real. These n real degrees of freedom
make all the difference!
Although less prevalent than their Hermitian counterparts,
complex symmetric matrices arise throughout
mathematics and its applications. For instance, suppose f
is holomorphic on D, with f(0) = 0 and f ′ (0) = 1. Then f
is injective if and only if for any distinct z 1 , z 2 , … , z n ∈ C,
the Grunsky-Goluzin inequality
n
z j z k
∑ w j w k log (
| j,k=1
f(z j )f(z k ) ⋅ f(z j) − f(z k )
)
z j − z k |
≤
n
∑
j,k=1
1
w j w k log
1 − z j z k
holds for all w = (w 1 , w 2 , … , w n ) ∈ C n . This is a Hermitiansymmetric
inequality:
|⟨Aw, w⟩| ≤ ⟨Bw, w⟩,
in which B = B ∗ is positive semidefinite and A = A T . In
applications, complex symmetric matrices have appeared
in the study of thermoelastic waves, quantum reaction
dynamics, vertical cavity surface emitting lasers, electric
power modeling, multicomponent transport, and the
numerical simulation of high-voltage insulators.
The most familiar result about complex symmetric
matrices is the Autonne-Takagi decomposition: if A ∈
M n (C) and A = A T , then A = UΣU T , in which U is unitary
and Σ is the diagonal matrix of singular values of A
(the square roots of the eigenvalues of the positive semidefinite
matrix A ∗ A). It was discovered by Léon Autonne
in 1915 and subsequently rediscovered throughout the
⎦
early twentieth century in various contexts: T. Takagi
(function theory, 1925), N. Jacobson (projective geometry,
1939), C.L. Siegel (symplectic geometry, 1943), L.-K. Hua
(automorphic functions of matrices, 1944), and I. Schur
(quadratic forms, 1945).
The innocent-looking Volterra operator
[Tf](x) = ∫ x f(y)dy
0
on L 2 [0, 1] is a familiar counterexample to many conjectures
made by budding operator theorists. For instance,
it has no eigenvalues and it is properly quasinilpotent:
‖T n ‖ 1/n → 0 and T n ≠ 0 for n = 0, 1, 2, …. It is a standard
example of a complex symmetric operator: T = CT ∗ C, in
which [Cf](x) = f(1 − x). Each element of the orthonormal
basis (e 2πinx ) n∈Z is fixed by C. With respect to this
basis, the Volterra operator has the matrix
⎡
⎢
⎣
⋱ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ . ..
⋯
i
6π
0 0 −
6π
i 0 0 0 ⋯
⋯ 0
i
4π
⋯ 0 0
⋯
− i
6π
− i
4π
0 − i
4π
i
2π
− i
2π
⋯ 0 0 0
⋯ 0 0 0
⋯ 0 0 0
− i
2π
1
2
i
2π
i
4π
i
6π
0 0 0 ⋯
0 0 0 ⋯
i
2π
−
2π
i
i
4π
0 − i
4π
i
6π
⋯
0 0 ⋯
0 0 − i
6π
0 ⋯
. .. ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱
in which the (0, 0) entry has been highlighted. This drives
home the fact that T is a rank-one perturbation of a
skew-Hermitian operator. One might jest that definite
integration is the study of a sparse, infinite complex
symmetric matrix!
Examples of complex symmetric operators abound. For
instance, every idempotent operator, normal operator,
truncated Toeplitz operator, and Hankel matrix is a
complex symmetric operator. What sort of properties do
they have?
An old result of Godič and Lucenko tells us that each
unitary U acting on a Hilbert space factors as U = CJ, in
which C and J are conjugations. This generalizes the fact
that a planar rotation is the product of two reflections. A
similar result holds for any complex symmetric operator:
if T is C-symmetric, then T = CJ|T|, in which J is a
conjugation that commutes with the positive operator
|T| = √T ∗ T.
There are occasional parallels between the Hermitian
and complex-symmetric worlds. This should be surprising
since many “poorly behaved” operators, like Jordan blocks
and the Volterra operator, are complex symmetric. The
celebrated Courant minimax principle asserts that if A
is an n × n Hermitian matrix, then the (necessarily real)
eigenvalues λ 0 ≥ λ 1 ≥ ⋯ ≥ λ n−1 of A satisfy
min max
codim V=k x∈V
‖x‖=1
x ∗ Ax = λ k .
On the other hand, Danciger’s minimax principle ensures
that if A = A T , then its singular values s 0 ≥ s 1 ≥ ⋯ ≥ s n−1
⋯
⎤
,
⎥
⎦
36 Notices of the AMS Volume 64, Number 1

satisfy
min
codim V=k
max Re x T Ax =
x∈V
‖x‖=1
⎧s 2k if 0 ≤ k < n 2 ,
⎨
⎩0 if n 2
≤ k ≤ n.
The peculiar singular value “skipping” phenomenon
occurs because of significant cancellation in the complexvalued
expression x T Ax. Naturally, appropriate generalizations
for compact operators exist.
We conclude with a complex-symmetric analogue of
Weyl’s criterion from spectral theory. Let σ(A) denote
the spectrum of a bounded linear operator T; that is, it
is the set of λ ∈ C for which T − λI does not have a
bounded inverse. If T = T ∗ , then λ ∈ σ(T) if and only if
there exist unit vectors x n such that
lim ‖(T − λI)x n‖ = 0.
n→∞
The familiar equation Tx = λx characterizes the eigenvalues
of T. A similar result holds in the complex-symmetric
setting. If T is C-symmetric, then |λ| ∈ σ(√T ∗ T) if and
only if there are unit vectors x n so that
lim ‖(T − λC)x n‖ = 0.
n→∞
In particular, the “antilinear eigenvalue problem” Tx =
|λ|Cx characterizes the singular values of T. This can
occasionally be used to obtain information about the
spectrum of |T| without computing T ∗ T itself.
References
[1] Stephan Ramon Garcia, Emil Prodan, and Mihai Putinar,
Mathematical and physical aspects of complex symmetric
operators, J. Phys. A 47 (2014), no. 35, 353001, 54 pp.
MR 3254868
Photo Credit
Photo of Stephan Ramon Garcia is courtesy of Pomona
College.
Stephan Ramon
Garcia
ABOUT THE AUTHOR
Stephan Ramon Garcia got his PhD
at UC Berkeley, worked at UC Santa
Barbara, and now teaches at Pomona
College. He is the author of two books
and over seventy research articles in
operator theory, complex analysis, matrix
analysis, number theory, discrete
geometry, and other fields. He has
coauthored over two dozen articles
with students.
January 2017 Notices of the AMS 37

THE GRADUATE STUDENT SECTION
The AMS Graduate Student Student Blog, Blog, by and by for and math for graduate math graduate students, students, includes puzzles includes and puzzles a variety and of
a variety of interesting columns. September 2016 featured the Lego Graduate Student, sampled below.
interesting columns. blogs.ams.org/mathgradblog.
blogs.ams.org/mathgradblog.
Checking that the coast is clear, the grad student
makes his third casual pass of the free cookies table
at the large exhibition stall.
Spotting multiple errors on his poster, the grad
student is almost relieved that nobody is looking at
his research.
Soaking in a committee member's advice, the grad student marvels at how the professor's random thoughts eclipse
several months of his dissertation work.
All images used with permission of the Lego Grad Student. See more of their work @legogradstudent on Facebook, Twitter, Instagram,
and Tumblr.
38 Notices of the AMS Volume 64, Number 1

AMERICAN MATHEMATICAL SOCIETY
Fan China
Exchange
Program
• Gives eminent mathematicians
from the U.S. and Canada an
opportunity to travel to China
and interact with fellow
researchers in the mathematical
sciences community
• Allows Chinese scientists in the
early stages of their careers to
come to the U.S. and Canada for
collaborative opportunities
Applications received before
March 15 will be considered for
the following academic year.
For more information on the Fan China Exchange Program and application process see
www.ams.org/employment/chinaexchange.html or contact the
AMS Membership and Programs Department by telephone at 800-321-4267, ext. 4113
(U.S. and Canada), or 401-455-4113 (worldwide), or by email at chinaexchange@ams.org

COMMUNICATION
My Year as an AMS Congressional Fellow
Anthony J. Macula
Each year, the American Mathematical Society (AMS), in conjunction with the American Association for the Advancement
of Science (AAAS), sponsors a Congressional Fellow who spends the year working on the staff of a Member of Congress or a
congressional committee, as a special legislative assistant in areas requiring scientific and technical input. The program
includes an orientation on congressional and executive branch operations and a year-long seminar series on issues involving
science, technology, and public policy. For information about applying for the Fellowship, visit the page bit.ly/
AMSCongressionalFellowship. The deadline for applications for the 2017–2018 Fellowship is February 15, 2017.
During the 2015–2016 academic year, I had the honor of
serving in the position of AMS Congressional Fellow, as
one of 284 AAAS Science and Technology Policy Fellows.
It was fun and exciting to engage with them on a broad
range of topics in science policy, advocacy, and diplomacy,
in both the natural and social sciences, and then to think
about how my mathematical training could be applied. I
ultimately took a somewhat mathematical approach in
drafting legislation in health, trade, and cybersecurity.
The Fellowship starts with a two-week “You are in
Washington, DC” orientation that included many exciting,
informative sessions (as well as some annoying though
probably necessary ones). Where else could one ask President
Obama’s chief science advisor about the President’s
feeling on a science issue, or the former presiding judge
of the Foreign Intelligence Surveillance Act (FISA) Court
what sort of technical advice and expertise the FISA Court
has at its disposal when deciding the legality of federal
surveillance programs? Another highlight was the daylong
“How Congress Works/Doesn’t Work” session by the
Congressional Research Service, a nonpartisan division of
the Library of Congress, which turned out to be a great
resource for me during my Fellowship.
Executive Branch Fellows know their federal agency
office placements before they arrive in DC, but Congressional
Fellows do not. To assign Fellows to Congressional
offices, the AAAS employs a process similar to match.
com. Congressional Fellows submit their profiles, and
Congressional offices submit their staffing needs. After
Anthony J. Macula is professor of mathematics at SUNY Geneseo.
His e-mail address is macula@geneseo.edu.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1466
orientation, the AAAS circulates these documents, and
the placement process begins with a “coming out” mixer,
where the two sides meet. Senators and Members of
Congress come to talk up their offices and their past
experiences with Fellows, while their aides mingle, looking
for the Fellows they feel will be a good match. After days
of e-mails and interviews, everyone is placed. I chose the
office of Congressman Jim McDermott because I felt that
he valued my professional and scientific background. I
was grateful to have a personal interview with the Congressman.
This isn’t so unusual, but many other Fellows
are interviewed only by staff.
Congressional offices employ Fellows in various ways,
and the position of a Fellow in the office’s chain of
command can vary from office to office. Congressman
McDermott was quite accessible to all his staff, including
Fellows. He felt that his office could learn from a Fellow
just as a Fellow could learn from his office, and together
we discussed many issues. I was asked to think about
higher education and trade issues that are brought before
the powerful House Ways and Means Committee of which
Congressman McDermott is a member. One of my tasks
was to prepare opinion papers for the Congressman to
consider. I was also allowed to work on some of my own
relevant interests, and I chose cybersecurity.
Orientation impressed upon us that getting the three
Ps—Policy, Procedure, and Politics—right was the way to
reach legislative nirvana. That is a tall order. Our chief of
staff encouraged me to press on, saying, “House Speaker
Paul Ryan can’t even get the three Ps to jibe within his
own House majority caucus.” The title of my year-end
presentation was, “Policy, Procedure, and Politics: 2+∈
Outta Three Ain’t Bad.”
I tried to extend the boundaries of existing law by
proposing scope-broadening amendments. I explained
this approach to the office by comparisons to complex
40 Notices of the AMS Volume 64, Number 1

COMMUNICATION
numbers and non-Euclidean geometry, and I felt that they
got a little insight into how a mathematician thinks.
I provided an argument in support of Senator Sanders'
College For All Act; Congressman McDermott became the
first co-sponsor of that bill. In addition, I drafted two bills
that Congressman McDermott introduced: “The Cybersecurity
Systems and Risks Reporting Act” and “Protecting
America’s Health Measures Act.” The first amends the Sarbanes–Oxley
Act of 2002 to protect the public by expanding
the requirements on public company boards, management,
and public accounting firms to include cybersecurity
systems and risks. It also stipulates that a publicly traded
company must appoint a cybersecurity specialist to its
audit committee. The second was introduced to improve
free trade agreements. The Trans-Pacific Partnership (TPP)
has a provision that protects anti-smoking measures from
investor-state dispute settlement arbitration. Our goal was
to extend this provision to apply to all US health measures.
This extension was a tricky thing to propose, because the
TPP can’t be directly amended. However, its implementing
mechanism can be, and this is what our bill does. It makes
explicit that protecting America’s health measures from
corporate trade lawsuits is an important trade negotiating
objective of the United States.
It is interesting to note that while the second bill has six
House cosponsors and the first has none, our chief of staff
felt that the first was more politically successful because
it received positive interest from some professional organizations
such as the American Institute of CPAs and it
was cited by some news organizations such as Bloomberg.
I am very grateful to the AMS for funding the Fellowship
and to the AAAS for the program support. It was an
enriching experience, and I feel that I am a better citizen
scientist, with a deeper understanding of policy and advocacy,
because of it.
Editors’ Note: The AMS Congressional Fellow for
2013–2014 was Karen Saxe, who was recently appointed
as director of the AMS Washington Office. Saxe wrote an
article about her Fellowship experiences that appeared
in the January 2015 issue of the Notices. The December
2016 issue of the Notices carried an interview with Saxe
upon her appointment as the new Director of the AMS
Washington, DC, office; the interview was conducted
by Notices Associate Editor Harriet Pollatsek.
Anthony J. Macula
THE AUTHOR
AmericAn mAthemAticAl Society
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January 2017 Notices of the AMS 41

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COMMUNICATION
AMS Waldemar J. Trjitzinsky Awards
Program Celebrates Its Twenty-Fifth Year
This year the American Mathematical
Society (AMS) celebrates
the twenty-fifth anniversary of the
establishment of the Waldemar J.
Trjitzinsky Memorial Awards.
These annual awards provide fellowships
to needy undergraduate
students in mathematics.
The program is made possible
by a bequest from the estate
of Waldemar J., Barbara G., and
Juliette Trjitzinsky.
Waldemar J. Trjitzinsky (1901–
1973) was a longtime member of
the mathematics department at the
University of Illinois at Urbana–Champaign.
He is remembered for his
notable contributions to mathematics,
mainly in quasi-analytic functions and partial differential
equations, and for the exceptional care he showed toward
students, for whom he sometimes made personal efforts
to ensure that financial considerations would not hinder
their studies. When his wife Barbara died, she left funds
to the AMS to create the awards program.
The Award
The AMS Trjitzinsky Awards Program runs in an unusual
way. There is no application process. Instead, each year
the Society randomly selects from its pool of institutional
members several geographically distributed institutions
to receive the awards. The mathematics departments at
those institutions in turn present one-time fellowships
to undergraduates, to help them on the path to careers
in mathematics. Knowing their students well, the departments
choose as fellowship recipients those for whom the
award will make a real difference. The brief biographies
of the Trjitzinsky Awardees, which appear in the Notices
each year, always make inspiring reading.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
Waldemar J. Trjitzinsky
The Man
Waldemar Joseph Trjitzinsky was born on March 9, 1901,
in Rostov-on-Don, Russia. Around the end of World War
I, he came to the United States and did his undergraduate
studies at the California Institute of Technology. He then
went to the University of California, Berkeley, where he received
his master's degree in 1925
and his PhD in 1926. His doctoral
thesis, written under the direction
of John Hector MacDonald, was
titled "The Elliptic Cylinder Differential
Equation."
After receiving his PhD, Trjitzinsky
taught at various institutions,
including the University of Texas
at Austin, Valparaiso University,
Lehigh University, and Northwestern
University. During 1930–32,
he was a National Research Fellow
at Harvard University, under the
supervision of G. D. Birkhoff. In
1934, Trjitzinsky accepted a position
at the University of Illinois,
where he remained for the rest of
his professional life.
During 1940–41, he spent a sabbatical at the Institute
for Advanced Study in Princeton. Later sabbaticals—in
1952, 1958, and 1962–63—were spent in Paris. Some
of his work was inspired by that of Arnaud Denjoy, and
presumably the two were in contact when Trjitzinsky was
in France. In addition to speaking Russian and English,
Trjitzinsky was fluent in French. Out of his forty-three
papers listed in Mathematical Reviews, twelve are written
in French. Birkhoff was Trjitzinsky's only co-author, and
the two wrote just one paper together, which appeared
in 1933.
In the Illinois mathematics department, Trjitzinsky was
known as “Tridgie.” He is the department's all-time leader
for the number of doctoral dissertations supervised; he
had a total of fifty-two PhD students. Among them were
Richard W. Hamming, known for the error-correcting
codes that now bear his name, and Richard A. Leibler,
who for many years directed the Institute for Defense
Analysis Research and Development Center in Princeton,
New Jersey.
Ken Fine was one of Trjitzinsky’s last PhD students,
finishing his degree in 1967. Fine had a thirty-year career
in industry and was, most recently, president and CEO
of Vivid Semiconductor. “When I think of Professor Trjitzinsky,
two things surpass everything else about him,”
Fine said. “He loved mathematics—that really was his
life. And he was just extremely caring.” Fine remembered
Trjitzinsky as an excellent teacher who, when he saw students
had trouble following one approach, could easily
change course and find a different one. As a thesis advisor,
44 Notices of the AMS Volume 64, Number 1

COMMUNICATION
he was always accessible and, more than that, enthusiastic
and excited about his students’ work. “I think he enjoyed
meeting with me as much as I enjoyed meeting with him,”
Fine recalled.
At the end of every semester, Trjitzinsky immediately
decamped to his vacation home in Mattapoisett, Massachusetts,
on Cape Cod. A few years after finishing his PhD,
Fine was working on the East Coast and decided to look
Trjitzinsky up in Mattapoisett. Fine had no idea where
Trjitzinsky’s house was, so when he saw a police officer
he described Trjitzinsky to him. Smiling, the officer said,
“Oh yes! The mathematician!” and told Fine where to go.
Answering the door, Trjitzinsky cried in surprise, “Fine!
It’s you!” Although perfectly presentable in nice trousers,
a white shirt, and a necktie, he quickly ran back inside to
put on his jacket. He had been sitting at a desk, working
on a mathematics paper.
That the AMS Trjitzinsky Awards should focus on
“needy students” in mathematics does not surprise Fine at
all. “That would be absolutely right in line with something
he would do,” he remarked. Fine has himself donated
funds to the Illinois mathematics department in memory
of Trjitzinsky. Another PhD student of Trjitzinsky, Bing
K. Wong, collected funds from Trjitzinsky students to
support the annual Trjitzinsky Memorial Lectures in the
department. In addition, Trjitzinsky's widow Barbara made
a bequest to the Illinois mathematics department, which
now supports graduate fellowships for needy students in
mathematics.
A member of the Society for forty-six years, Trjitzinsky
served on the AMS Council from 1938 to 1940, and he
delivered two Invited Addresses at Society meetings. He
retired from the University of Illinois in 1969. His career
in mathematics and teaching ended with his death on
December 8, 1973, in Mattapoisett, where he lived after
his retirement from the University of Illinois.
—Allyn Jackson
2016 Trjitzinsky Awardees
For the 2016 awards, the AMS chose seven geographically
distributed schools to receive one-time awards of
US$3,000 each. The mathematics departments at those
schools then chose students to receive the funds to assist
them in pursuit of careers in mathematics.
What follows are the names
of the schools receiving the 2016
AMS Trjitzinsky Awards, and the
names and biographical sketches
of each school's chosen awardee.
Colorado State University at
Pueblo: Andrew D. Coleman.
Andrew is from Pueblo, Colorado,
and is one of the up-and-coming
math majors at Colorado State
University—Pueblo. Intrigued by
calculus, he decided to pursue
a mathematics degree, and then
Andrew D. Coleman found a love for number theory
and linear algebra. He looks forward to learning more in
these areas in particular. Recommended by professors, he
landed a job in the Math Learning Center (MLC), a campus
math tutoring room. Working in the MLC has honed his
math skills and has given him the opportunity to tutor
students in physics as well. He has now added a minor
in general engineering and reports that these courses
are also heightening his physics knowledge, broadening
his general understanding of the applications of mathematics.
Rutgers University: Terence
Coelho. Terence is a junior mathematics
and computer science
double major at Rutgers University.
He held an interest in mathematics
from a young age, but it
wasn’t until he immersed himself
entirely in the subject during his
first year at college that he realized
how much he loved mathematics.
He then made his new
goal attending graduate school
Terence Coelho
and pursuing a career in pure
mathematics. He has done research
in combinatorics and is currently working on a
project in algebra. He also works as freelance math tutor
and grading assistant.
San Francisco State University:
Edwin Garcia. Mathematics
had always been Edwin’s favorite
subject since he first learned the
times tables in Spanish. During
his senior year in high school, he
took an AP statistics course and
enjoyed the method and functionality
that statistics used to solve
problems; it became his favorite
math class. He found learning
how to properly read data and
Edwin Garcia
knowing exactly what to do with
it in order to find out its meaning
exciting—this is why he decided to major in statistics at
SFSU. Edwin worked as a tutor for two years at Francisco
Middle School, located in San Francisco, where he helped
students struggling in math and any English-learning
students who spoke Spanish. His
parents immigrated to the United
States so that they could have a
better life but also so their family
would have all the benefits they
did not have in Mexico. Edwin
is excited to make his parents
proud as their first child to graduate
from college.
Texas Christian Un iversity:
Seth Erik Emblem. Seth is a senior
mathematics-actuarial,
economics, and philosophy triple
major pursuing a BA degree in
Seth Erik Emblem
January 2017 Notices of the AMS 45

COMMUNICATION
mathematics-actuarial science and a BS degree in economics.
Since the beginning of his college career, he has
been interested in how his three fields of study intertwine
and how they collectively can solve complex problems in
the world. He had an actuarial internship over the past
summer at Texas Farm Bureau Insurance in Waco, Texas.
He plans on using his degree to pursue employment in
the actuarial field, but he is also interested in the study
of happiness as a mathematical, economical, and philosophical
concept.
University of North Texas:
Madison C. Dupont. Madison
comes from a military family and
developed a passion for mathematics
at an early age. She has
been active in the math community,
tutoring over the duration of
her high school years and, more
recently, teaching conceptual
mathematics with Mathnasium
Learning Centers in her community
of Allen, Texas. She is a proud
Madison C. Dupont
mother and a motivated student.
Madison holds a senior status at
the University of North Texas, where she is a member
of the Teach North Texas program and is pursuing her
mathematics bachelor’s degree. She will graduate in December
2017. Her aspiration for a mathematics degree is
to reach the young minds of our nation and to promote
the approachability and the importance of mathematics
through secondary mathematics education.
University of Tennessee at
Chattanooga: Breana Kechelle
Leach. Breana graduated from
Bolton High School in Memphis,
Tennessee, in 2012, with the
intent to study nursing at the
University of Tennessee at Chattanooga.
However, after tutoring
mathematics and statistics
to college students and working
as a high school teacher’s assistant,
she developed an interest
Breana Kechelle
Leach
in teaching these subjects. With
this in mind, Breana changed her
major as a college junior to general
mathematics and intends to earn a master’s degree
in mathematics and statistics. Overall, her career goal is
to teach mathematics courses in public city schools and
introduce the foundations of statistics to inner-city youth
who may otherwise not have such an opportunity.
Support the Trjitzinsky Awards Program
More information about the AMS Waldemar J.
Trjitzinsky Memorial Awards program can be found
at www.ams.org/trjitzinsky. Donations to the
AMS in support of the Trjitzinsky Awards continue
to be encouraged and accepted; they allow the AMS
to fund more deserving undergraduate students who
are studying mathematics. Information on donating to
the AMS can be found at www.ams.org/support-ams.
Virginia Commonwealth University:
Renee Adonteng. Renee
is currently a junior at Virginia
Commonwealth University and a
mathematical science major with
two concentrations, in applied
mathematics and pure mathematics.
Growing up, Renee always
loved math. She feels that mathematics
is straightforward and
there’s no way of going around the
answer: The certainty is refreshing
because the answer will never
Renee Adonteng
change. She is very interested in
working in risk insurance and would love a career in actuarial
science. Renee would also like to become a college
professor and also give back to the community and teach
or tutor children who may be having trouble in math.
—From the AMS Trjitzinsky Fund announcement
Photo Credits
Photo of Waldemar J. Trjitzinsky is courtesy of Department
of Mathematics, University of Illinois at Urbana–
Champaign.
46 Notices of the AMS Volume 64, Number 1

BOOK REVIEW
Origins of Mathematical
Words
A Review by Andrew I. Dale
Origins of Mathematical Words: A Comprehensive
Dictionary of Latin, Greek, and Arabic Roots
Anthony Lo Bello
Johns Hopkins University Press, October 2013
US$51.95, 368 pages
ISBN-13: 978-1-4214-1098-2
There are many reasons for picking up a dictionary
beyond finding information, such as the meaning and
derivation of a word. For example, Brewer’s Dictionary of
Phrase and Fable provides esoterica like the names and
dates of the kings and queens of England, while Ambrose
Bierce’s Devil’s Dictionary
supplies amusement and
This is a
book one
may read
and not just
consult
wit. In addition to the once
useful task of removing a
ganglion cyst by a smack
with a heavy tome, a dictionary
in the hand, as opposed
to one accessed via
a computer, tablet, or cell
phone, has the benefit that
one hardly ever finds the
word one wants straight
away. This exposes one to the pleasure of finding other
words that in themselves may well be interesting. To a
greater or lesser degree the Origins of Mathematical Words
(OMW) contains information, esoterica, and humour.
“This is a book about words, mathematical words, how
they are made and how they are used,” Lo Bello writes in
the preface. While most entries in the OMW are comparatively
short, some—such as Archimedes, cant, Descartes,
Euclid, [teaching] evaluation (an excellent discussion),
Andrew I. Dale is emeritus professor of statistics at the University
of KwaZulu-Natal in Durban, South Africa. His e-mail address is
dale@ukzn.ac.za.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1468
Timaeus—are almost short essays. It is a book one may
read and not just consult.
I found here many words that I had not come across
before and some that I suspect have almost disappeared
from modern mathematical usage, though Lo Bello says,
“I have written this dictionary to describe the current vocabulary
of our subject.” While he cites certain words in
mathematics that were introduced by the Arabs and that
have survived, there are of course terms that were introduced
but have not survived. As examples of the latter Lo
Bello mentions some words introduced by Boëthius, such
as œthimata (postulates) and oxygonium (acute-angled).
I would mention the nineteenth-century mathematician
Augustus de Morgan, who used the almost completely
forgotten words comminuent, invelopment, generata, and
generatrix, though the latter has survived to some degree
in geometry.
Lo Bello not only gives the Latin, Greek, and Arabic
derivations and formations of mathematical words but
also, when he finds terms to be erroneous, suggests formations
that would be correct. For example, concentric
has a Latin beginning and a Greek ending: more correct
would be the Greek syncentric or the Latin concentral. He
also writes that Cantor’s “use of Hebrew letters was a bad
idea, as one can scarcely expect people to write legibly in
their own language, let alone in Hebrew.”
The passage (and the preservation) of mathematics is
traced first from the Greeks to the Romans, then to the
Arabs, and then back to Rome. An advantage that Lo Bello
has wisely passed on to his reader is that the origins of
Greek and Arabic words are given here in the original
alphabets, thus eliminating any queries about transliteration.
Indeed, while extolling some arguments in favour
of transliterations, Lo Bello also writes, “They are also
employed when the translator is intellectually limited and
does not understand what he is translating.’’
Mathematics itself enjoys a long essay in the OMW, and
its derivation from the Greek µαθηµα—meaning learning,
knowledge, or study—is noted. However, Lo Bello’s aim is
January 2017 Notices of the AMS 47

Book Review
not restricted to the bull’s eye of the mathematical target,
for he writes:
I have sat in judgment on the correctness of the
words I explain, and I have used my license to
be discursive to discuss not only the function
of mathematics in liberal education but also
English usage among mathematicians and their
colleagues in the learned world.
He disapproves of words like “pro-active” and even “neuroscience,”
and in connection with English grammar he
writes:
And:
Usages such as unnecessarily splitting infinitives
or using politically correct terminology
become established practices that it is considered
old-fashioned or offensive to criticize.
Rules of grammar in the literary world are like
protocol in the social world; protocol keeps in
their place people who do not know their place.
stance goodness is good, but wellness sits ill, despite the
growth of its use. Is there a cure for the proliferation of
such monstrosities? “The only solution,” declares Lo Bello,
“is education,” an opinion he follows up with a discussion
of the purposes, both positive and negative, of education.
The careful writer in English can make good use of
Fowler’s Modern English Usage, but one must take note
that the latest edition of this incomparable work, from
2004, has at least one entry that may well have a deleterious
impact on mathematical writing, namely, the entry
for parameter:
A mathematical term of some complexity
which, in the course of the 20c., has become
perceived by the general public as having the
broad meaning “a constant element or factor,
esp. serving as a limit or boundary.’’
So parameter means the same thing as perimeter ? I
have also noted with dismay the use made currently of
words like quantile and percentile to denote areas under
a curve rather than points on an axis, though the former
usage is sanctioned by the OED.
Should we care a fig for general public
perceptions of such technical terms? One
might fight against the wrong use, but once
sufficient leverage is gained, correct usage
is viewed at best as an amusing idiosyncrasy.
And no matter how loath one might
be to accept this, with the passage of time
and human perversity words acquire new
meanings and become “good” English. I
am sure there are many words that I am
all too ready to use that were regarded as
completely unacceptable a century ago.
Lectures in mathematics and statistics
are, I believe, enhanced, at least for the
good student, by the mention of the historical
development of results and terminology,
and the OMW will be of great use
in this. Sad to say many of the corrections
Lo Bello suggests will be ignored: I cannot,
for instance, see statisticians opting for
kyrtosis rather than kurtosis or for ceasing to say regress x
on y (although regress should be used intransitively) any
more than I can see educationists eschewing numeracy.
Nevertheless, I can heartily recommend the OMW for all
who like to know what they are writing or talking about.
Three of my personal pet aversions are the use
of their as a singular pronoun (also discussed
by Lo Bello); facilitator (pure cant, in Lo Bello’s
opinion); and icon, with the implication that the
person to whom it is applied is worthy of veneration.
However, we must accept neither the
Oxford English Dictionary nor Merriam-Webster
as the final arbiter on matters of language: there
is in fact a long article in the OMW on American
spelling and Noah Webster’s “crimes.” Lo Bello
himself writes, “The fact that a word appears
in the Oxford English Dictionary does not imply
that it is a good word... The sanction of existence
can only be imparted to a word through
its use by a polished author.’’
English dictionaries are often partly prescriptive
and partly descriptive: that is, they note
how words should be used and also how they
are used. Lo Bello himself is not always among
the prescriptive rather than the descriptive dictionarists.
For example, in his entry Euclidean he notes that
“To write euclidean with a small e is not a practice of the
best authors and is therefore not correct.” The difficulty,
of course, is deciding who are the best authors. Lo Bello
notes “the precariousness of forming new words according
to rules from foreign languages without reference to the
usage of the first class of writers.” Leibniz is viewed as a
suitable authority, at least on the use of analysis situs, a
phrase with a Greek nominative and a Latin genitive—or
am I missing an irony? (Perhaps not, since Lo Bello writes,
“Levity is unbecoming to mathematics.”) And the use of
binomial is sanctioned by Newton, though Lo Bello considers
multinomial and polynomial to be “low.”
When it comes to modern words of the twentieth and
twenty-first centuries, Lo Bello says, “Such compositions
are frequently acronyms or macaronic concatenations, the
infallible sign of defective education.’’
In a similar vein one must guard against the attaching
of “ness” to adverbs rather than adjectives. Thus for inonce
sufficient
leverage
is gained,
correct
usage is
viewed at
best as an
amusing
idiosyncrasy
ABOUT THE REVIEWER
Andrew Dale studied at the University
of Cape Town and the
Virginia Polytechnic Institute and
State University. He spent some
forty years lecturing at the University
of Natal (later the University
of KwaZulu-Natal) and has a keen
interest in the history of statistics
and probability.
Andrew I. Dale
48 Notices of the AMS Volume 64, Number 1

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BOOKSHELF
A man is known by the books he reads. —Emerson
New and Noteworthy Titles on Our BookShelf
January 2017
The Magic of Math: Solving
for x and Figuring Out Why,
by Arthur Benjamin (Basic
Books, September 2015).
In 2000, the Mathematical
Association of America
presented its Haimo Award
for Distinguished College
or University Teaching of
Mathematics to Arthur
Benjamin. And this year, he is receiving the Communications
Award of the Joint Policy Board for Mathematics, for
his work in public outreach. These two roles, as outstanding
teacher and math proselytizer, come together in his
latest book, The Magic of Math. The book is an outgrowth
of his video course “The Joy of Mathematics,” produced by
Great Courses. In addition to being a mathematics professor
at Harvey Mudd College, Benjamin is a professional
magician and gives dozens of performances a year as a
“mathemagician,” doing lightning fast calculation tricks
and other mental feats. While exuding all the pizazz and
appeal of a professional entertainer, Benjamin aims in the
book to show that in mathematics there are no tricks, no illusions,
no sleights of hand, and that what is really magical
in mathematics is its beauty. The book has twelve chapters
focusing on such topics as the integers; algebra; Fibonacci
numbers; geometry; the numbers i, π, and e; and calculus.
The closing chapter is “The Magic of Infinity.” Sprinkled
here and there in the book are explanations of mental
math tricks that readers can use to impress their friends,
as well as to deepen their mathematical understanding.
Aimed at a wide audience, The Magic of Math would be
accessible to just about anyone. Benjamin’s unpretentious,
humorous authorial voice invites readers to relax
and have fun. According to a review in Publisher’s Weekly,
“[the book’s] energy and enthusiasm should charm even
the most math-phobic readers.” An interview with Arthur
Benjamin appears in the Graduate Student Section of this
issue of the Notices. (See p. 32)
Suggestions for the BookShelf can be sent to noticesbooklist@ams.org.
We try to feature items of broad interest. Appearance of
a book in the Notices BookShelf does not represent an
endorsement by the Notices or by the AMS. For more, visit
the AMS Reviews webpage www.ams.org/news/math-inthe-media/reviews.
Prof: Alan Turing Decoded, by
Dermot Turing (The History
Press, September 2015). In
1983, Andrew Hodges published
to wide acclaim his
monumental biography Alan
Turing: The Enigma. Since
then—and especially in conjunction
with the centenary
of Turing’s birth in 2012—the
story of his life has been told
and re-told in various media, including the popular film
The Imitation Game. In 2015, an unusual contribution to
the literature about Turing appeared: Prof: Alan Turing
Decoded, written by his nephew, Dermot Turing. Although
the book is a personal account, author and subject never
met: the son of Alan Turing’s older brother John, Dermot
was born in 1961, seven years after Alan’s death. Nevertheless,
Dermot’s book offers some new insights. Like
his uncle, he attended Sherborne School and Cambridge
University. After receiving a doctorate in genetics at
Oxford, he moved into the legal profession. He is a trustee
of the Bletchley Park Trust, which is dedicated to preserving
the history of the extraordinary code-breaking operations
that Alan Turing and others carried out during World
War II. Dermot Turing’s book draws on many unpublished
documents and photographs available to him through his
family and through Bletchley Park. “What results is a cheerfully
anecdotal account of a slightly grubby, surprisingly
athletic, formidably clever and pleasingly humorous and
humane man,” writes Clare Mully in a review in the February
2016 issue of History Today. While the book says that
the dominant passion in Alan Turing’s life was ideas, it
focuses less on those ideas and more on a personal portrait
of Turing the man. As Mully notes: “[T]his is not an
academic book and should perhaps be read with a glass
of wine at hand.” Dermot is not the only Turing to have
written about the genius in the family. In 1959, Sara Turing
published a biography of her son Alan. In the twenty
years that followed, her elder son John worked on his own
account of his brother’s life. The memoir John produced
was found after his death by his son Dermot and included
in the 2014 edition of Sara’s biography. Condensed versions
of John’s frank and fascinating memoir are available
on the internet, for example on the website of The Atlantic,
under the title “My Brother the Genius.”
50 Notices of the AMS Volume 64, Number 1

NEWS
Mathematics People
Kida Awarded Operator
Algebra Prize
Yoshikata Kida of the University
of Tokyo has been awarded
the fifth Operator Algebra Prize
“for his outstanding contributions
to the interaction between
ergodic theory and geometric
group theory, and applications
to theory of operator algebras.”
The Operator Algebra Prize was
established in 1999 by initiatives
and contributions from
Yoshikata Kida
some senior Japanese researchers
in operator algebra theory
and related fields to encourage young researchers. The
prize is awarded every four years for outstanding contributions
to operator algebra theory and related areas
to a person under forty years of age either of Japanese
nationality or principally based in a Japanese institution.
The prize consists of a cash award of about US$3,000, a
prize certificate, and a medal.
—Yasuyuki Kawahigashi, Chair,
Operator Algebra Prize Committee
Nisan Awarded Knuth Prize
Noam Nisan
Noam Nisan of the
Hebrew University of
Jersalem has been
awarded the 2016 Donald
E. Knuth Prize “for fundamental
and lasting contributions
to theoretical
computer science in areas
including communication
complexity, pseudorandom
number generators,
interactive proofs, and
algorithmic game theory.” The prize citation reads in
part: “Nisan’s work has had a fundamental impact on
complexity theory, which examines which problems could
conceivably be solved by a computer under limits on its
resources, whether it is on its computation time, space
used, amount of randomness or parallelism. One of the
major ways in which computer scientists have explored
the complexity limits is through the use of randomized
algorithms. Nisan has made major contributions exploring
the power of randomness in computations. His work
designing pseudorandom number generators has offered
many insights on whether, and in what settings, the use
of randomization in efficient algorithms can be reduced.”
The Knuth Prize is given jointly by the Association for
Computing Machinery (ACM) Special Interest Group on
Algorithms and Computation Theory (SIGACT) and the
Institute of Electrical and Electronics Engineers (IEEE)
Computer Society Technical Committee on the Mathematical
Foundations of Computing (TCMF). The award carries
a cash prize of US$5,000.
—From an ACM announcement
Rothvoss Awarded 2016
Packard Fellowship
Thomas Rothvoss of the University
of Washington has been
awarded a Packard Fellowship
by the David and Lucile Packard
Foundation. The Fellowship provides
a grant of US$875,000 over
five years to allow the recipient
to pursue his or her research.
Rothvoss works in computer
and information sciences. His
research deals with the question
Thomas Rothvoss of which types of computational
problems can be solved efficiently
by algorithms and which ones cannot. In particular,
he develops techniques to find approximate solutions to
52 Notices of the AMS Volume 64, Number 1

Mathematics People
NEWS
computationally hard problems. He tells the Notices: “I
did my undergraduate studies in computer science back
in Dortmund, Germany. But quickly I got fascinated by
questions in particular in complexity theory and I gave
up my goal of getting a real job, turning to mathematics
and theoretical computer science research. To get my
head free, I like hiking in the Pacific Northwest as well
as biking.”
—From a Packard Foundation announcement
Morrison Awarded Australian
Mathematical Society Medal
Scott Morrison of the Australian
National University
has been awarded the 2015
Australian Mathematical Society
Medal for his research
in Khovanov homology, derived
topological quantum
field theories, and small examples
of subfactors and
tensor categories. Morrison
Scott Morrison
is one of the founders of
MathOverflow and a member
of the arXiv’s mathematics advisory board. He tells the
Notices: “I’m really excited about quantum symmetries,
tensor categories, and topological matter!” The medal is
awarded annually to a member of the Society under the
age of forty for distinguished research in the mathematical
sciences, a significant portion of which should be carried
out in Australia.
—From an ANZIAM announcement
Photo Credit
Photo of Yoshikata Kida is courtesy of Yasuyuki Kawahigashi.
Photo of Noam Nisan is courtesy of Rotem Steinitz-Nisan.
AmericAn mAthemAticAl Society
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The text rapidly introduces problems in Diophantine geometry,
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In some instances, proofs have been replaced by a detailed analysis
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Siegel’s finiteness theorem for integral points on curves plays a
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January 2017 Notices of the AMS 53

COMMUNICATION
Aleksander (Olek) Pelczynski
1932–2012
Edited by Joe Diestel
Aleksander Pelczynski was a leader in functional analysis
for more than half of a century.
Olek (as he was known to most who knew him) worked
in Banach space theory much of his later life but previously
made serious contributions to infinite dimensional
topology and the theory of nuclear Frechet spaces. He
kept in touch with workers in all these vineyards and was
frequently an inspiration to young workers with keen insights
and suggestions. He was famous for his signature
question, “What did you prove last night?”
Olek wrote many papers now considered to be classics.
In the seventies he concentrated on how Banach space theory
interfaced with harmonic analysis, complex variables,
and probability. He frequently expressed the opinion that
Banach space theory was an area that needed to “test its
wares in other areas of mathematical endeavor” and, as
was usually the case, he was a leader in such efforts.
Joram Lindenstrauss, R. C. James, and Aleksander
“Olek” Pelczynski.
Joe Diestel is emeritus professor of mathematics at Kent State
University. His e-mail address is vectormeasurejoe@gmail.com.
I had the help of many in organizing this ode to Olek, including
Nicole Tomczak, Hermann Konig, Stan Kwapien, Tadek Figiel,
Czeslaw Bessaga, Darci Kracht, and Angie Spalsbury.
For permission to reprint this article, please contact:
reprint-permission@ams.org.
DOI: http://dx.doi.org/10.1090/noti1464
For many years Olek was the main line of communications
between functional analysts from the East and West.
Many will remember a one-page statement and proof of
Victor Lomonosov’s startling theorem on invariant subspaces.
This page was the result of Olek’s dictating the
result to Czeslaw Bessaga, who was in the United States
at the time, and requesting that Czeslaw make copies and
send them to “our friends in America.”
Stan Kwapien tells of Olek’s early academic life:
In 1950 Olek, along with Czeslaw Bessaga and Stefan
Rolewicz, participated in the Mathematical Olympiad for
high school students, which was organized in Poland for
the first time. Later at the University of Warsaw they met
an exceptional team of teachers, including Banach’s closest
collaborator, Stanislaw Mazur, whose seminar had a decisive
impact on their future mathematics. As a PhD student
(1957–58) Olek published fourteen papers, six jointly with
Bessaga and one jointly with Bessaga and Rolewicz. One of
these papers with Bessaga, “On bases and unconditional
convergence in Banach spaces,” is one of the most cited
papers in functional analysis and is considered by many
to be a classic in the area. Olek defended his dissertation
in December 1958 after a trip with Orlicz to China, a reward
for his achievements in mathematics. For Olek this
trip was unforgettable, a trip “to the end of the earth.” It
is quite likely that the visit contributed to the decision of
the Chinese government to implement functional analysis
in the basic Chinese curriculum.
Boris Mityagin remembers Olek’s time in the Soviet
Union:
In November of 1959, Pelczynski came to Moscow State
University for a half year as a visiting researcher. At the
time he was interested in problems on nuclear spaces
initiated by Kolmogorov and Gelfand. In 1955 Kolmogorov
introduced invariants for Frechet spaces based on the
growth of compact sets (entropy) in a space. Pelczynski
suggested closely related invariants, later called approximative
and diametral dimension. These helped explain
why various spaces of differentiable functions were mutually
isomorphic or not.
I recall fondly when our families spent the summer of
1975 together in Peredelkino near Moscow. Olek’s daughter,
Kasis, 5, spoke Russian with her mother Svetlana and
that summer perfected her skill with the Russian language.
54 Notices of the AMS Volume 64, Number 1

COMMUNICATION
(Today Katarzyna Pelczynski-Nalecz is Polish ambassador
to Russia.) At that time Olek and I succeeded in showing
that the Banach spaces of functions analytic in the m-disc
and continuous on the boundary were nonisomorphic for
different m. This was a step in a long series of results due
to Henkin, Kisliakov, and Bourgain on the isomorphic
classification of Banach spaces of analytic or differentiable
functions.
Vitali Milman recalls an encounter with Olek while
in the Soviet Union:
Around 1968 I was living near Moscow and came to the
university to meet Olek. During our conversation Olek said
to me, “We are very concerned with the proof of Dvoretzky’s
theorem and think there is a gap in its proof.” The
“we” being Joram Lindenstrauss and Olek. Since I was very
interested in applications of Dvorezky’s theorem, the gap
meant many of my results were conditional. However, I
thought I knew how to give a full and correct proof and
said so to Olek, to which he replied, “Then do it.” Olek’s
push inspired me to write down my proof, something that
as a young mathematician I was somewhat intimidated to
do—write down the proof of a known result.
Albrecht Pietsch:
Our most important joint
1969 was a
wonderful
year for
the theory
of Banach
space
geometry
interest was operator ideals.
At the Moscow IMU Congress
1966, Mityagin and Pelczynski
delivered a half-hour report
on “Nuclear operators and
approximative dimension,”
in which the concept of a
(p, q)-absolutely summing operator
was introduced. Many
years later, it was my great
honor for me to act as chairman
for Olek’s famous onehour
plenary lecture, “Structural
theory of Banach spaces
and interplay with analysis and probability,” at the 1983
Warsaw IMU Congress.
D. J. H. “Ben” Garling:
1969 was a wonderful year for the theory of Banach
space geometry. In the previous year, Joram Lindenstrauss
and Olek Pelczynski had published their seminal paper,
which elucidated and built upon Grothendieck’s work of
the 1950s. In the summer of 1969, a meeting in Warsaw
brought together these results and the ideas of Laurent
Schwartz and his school concerning measures on Banach
spaces and Radonifying operators. The outcome was explosive
and the reverberations continue to this day.
Bill Johnson:
The two architects of modern Banach space theory,
Joram Lindenstrauss and Olek Pelczynski, both left us in
2012. I met Olek first, in 1971 when he spoke at Tulane
University. After a brief exchange of pleasantries, Olek
asked me, “What have you proved?” I learned later that
this was his standard greeting. I hated it when we were
W. B. Bill Johnson, Pelczynski, and Tadek Figiel.
together for some time and I had to answer “nothing”
each morning.
My first paper with Olek, which was written jointly with
W. Davis and T. Figiel, contained a result that is now in
textbooks, namely, that a weakly compact bounded linear
operator factors through a reflexive Banach space. Olek
was not content with just this basic theorem and pushed
to use the interpolation technique we employed to prove
other results. This taught me a lesson about being professional:
before turning to a different topic, one should
work out the ramifications of the arguments and ideas.
I was pleased to learn from Google Scholar that this factorization
publication is Olek’s third most cited paper
after his “Absolutely summing operators in L p -spaces
and their applications” paper with Joram and his “On
bases and unconditional convergence of series in Banach
space” article with Bessaga. I especially appreciate his
series of papers with various people on the isomorphic
structure of the Banach spaces C(K). Recently I had occasion
to go back to several of these and once again marveled
at what he and his collaborators proved at a time when
the isomorphic theory had few tools.
The year Olek spent at Ohio State in the 1970s was
exciting for the analysts in Ohio. Much of his time was
spent preparing for his CBMS lectures in Kent in July 1976.
Pelczynski and Jean Bourgain at Oberwolfach in the
summer of 1986.
January 2017 Notices of the AMS 55

COMMUNICATION
Olek’s book
...represents
what was at
the time an
amazingly
original
and seminal
collection of
insights
The manuscript he produced
for the CBMS regional conference
series, “Banach spaces
of analytic functions and absolutely
summing operators,”
helped bridge what was then
a wide gap between classical
and functional analysis. From
then until the very end, Olek
devoted his time investigating
spaces of interest to classical
analysts, such as Sobolev
spaces and spaces of functions
of bounded variation.
Jean Bourgain:
In 1979, as a member of my
habilitation committee at the
Free University of Brussels,
Olek praised my work but
made it clear that a few in the
field had produced superior theses and that in his view it
was time for me to work on something else. So I borrowed
his Banach Spaces of Analytic Functions and Absolutely
Summing Operators from my advisor and asked which of
the many problems had been solved and which were still
open. Fortunately, there were plenty of unsolved questions
left, and they became my research focus for the early eighties.
More importantly, they naturally led to my in-depth
study of various topics in classical analysis. Olek’s book
lies indeed at the interface of classical function theory and
functional analysis and represents what was at the time
an amazingly original and seminal collection of insights.
Some problems got solved; some remain open until today.
Most notorious perhaps is the issue of whether or not the
space of bounded analytic functions on the disc has the
approximation property. In his book Olek did not express
himself one way or the other, but he did so privately (and
our views differed).
Discussions with Olek were invariably entertaining because
of his highly personal views on many issues in and
outside math and his direct way of expressing his frank
opinions. I recall him making the comment on more than
one occasion, “If you want a real achievement, you should
not have a survivor’s mentality” (though it was never quite
clear to me what the second part of the sentence means
for a mathematician).
Hermann Konig:
In 1968, Olek published (jointly with Joram Lindenstrauss,
who sadly also died in 2012) one of the most
important papers in Banach space theory, “Absolutely
summing operators in L p -spaces and their applications.”
This paper reformulated Grothendieck’s results in “Resume
de la theorie metrique des produits tensoriels topologiques”
in tensor product-free language and solved
various open problems in Banach spaces. It launched the
local theory of Banach spaces based on uniform estimates
of finite-dimensional invariants, rejuvenated the area of
Banach spaces, and resulted in an outburst of activity in
Banach spaces and operator theory.
Olek had an encyclopedic knowledge of functional analysis
and related areas and a keen interest in new results.
“What did you prove recently?” was one of his typical
comments. He had an incredible memory to reproduce
proofs he had once read or heard about.
Before the fall of the iron curtain Olek was one of the
few mathematicians who were able to travel rather freely
from Poland to the West and throughout the East. He was
in a unique position to communicate new ideas between
the East and the West.
Olek had a dry sense of humor, which showed at times
when he expressed everyday events in mathematical
terms. Once coming from Warsaw by train to Kiel he had
to pay 25 Marks for the ticket from the East-West German
border and 24 Marks for the return trip. He concluded that
“the German railway system is noncommutative.”
Nicole Tomczak-Jaegermann:
I met Professor Pelczynski in the mid-sixties when I
was a second year student at Warsaw
University. At that time I was trying
to find mathematics that I liked. I visited
Pelczynski’s functional analysis
lectures a few times and then stayed.
When the time for exams came in
the spring, my third year colleagues
suggested I ask for an exam and get
credit for the course a year in advance.
Pelczynski agreed and we walked
together to the Palace of Culture. I
Nicole Tomczak-
Jaegermann
remember that this approximately
two kilometer walk took about an
hour and on the way I had to answer
a pile of apparently casual questions covering almost
all the material of the course. This turned out to be just
the beginning: after arriving at his office in the Palace,
Pelczynski informed me, “Now the exam starts!” I passed.
While I was working on my doctorate I was invited to
Poznan to give a lecture. After the lecture there were some
questions and at the end, Professor Musielak, who was my
host, remarked that it was very obvious whose student I
was: all the problems I was working on were either open
or trivial.
Tomek Szankowski:
When I started my undergraduate studies in 1963 the
mathematics in Warsaw was still dominated by the celebrities
of the pre-war Polish school centered on point set
topology and set theory. Pelczynski was then an “angry
young man,” vigorously trying to modernize the teaching
and research of analysis in Warsaw. For example, he
created quite a panic when he decided to teach advanced
calculus the Bourbaki way; this was the most memorable
course of my undergraduate study. On the research
level, Olek was then pursuing two big projects: infinite
dimensional topology (working closely with Bessaga) and
operator ideals (as a tool for Banach space theory). In both
areas he made major contributions. His book with Bessaga,
Selected Topics in Infinite-Dimensional Topology, is the
ultimate text on the subject, while his paper with Joram
56 Notices of the AMS Volume 64, Number 1

COMMUNICATION
Pelczynski lecturing at Kent State.
Lindenstrauss has been a most influential contribution to
Banach space theory.
I got to know Olek personally through an undergraduate
seminar on “Extensions and Averagings.” I managed to
solve an open problem he posed in the seminar and was
very conceited about it. Olek brought me back to reality
with the wry remark, “Still, you are no Grothendieck.”
But, of course, it was only his style; as an advisor he was
extremely supportive, stimulating, and also demanding.
Regularly my telephone woke me up at 8 am: “What have
you proved today?” was the standard question.
For years to come I kept meeting Olek at various conferences,
always being asked, “What have you proved
recently?” Recently I asked him a technical question, one
that had puzzled me for some time. The next morning
he had a solution. Mathematics was always the first and
main topic of his conversation. Only when he’d exhausted
the discussion on this would he change the topic, usually
to history, his great hobby. I will miss these lively and
entertaining conversations.
Niels Nielsen:
I met Olek for the first time in 1968 when he visited
Aarhus University in Denmark. I discussed a lot of mathematics
with him and was struck by how easy it was to
communicate with him and how much care he took of a
young person. This had an enormous impact on the rest
of my mathematical life.
To many people Olek could seem a bit impractical, but
when it came to important things he was very efficient.
If a bureaucrat told him something was impossible he
would take the mathematical attitude and with his dry
humor claim, “Your statement requires proof!” After some
discussion most bureaucrats would give up.
I visited him in Warsaw in the late 1980s. Olek greeted
me with, “Welcome to free Poland!” and together we celebrated
the downfall of the communist regime in Poland,
a thing not expected in our lifetime.
Carsten Schutt:
Olek was one of the reasons I chose Banach space
theory as my field of research. His Studia Mathematica
paper with Joram Lindenstrauss on “Absolutely summing
operators in L p -spaces and their applications” explained
much of Grothendieck’s work in functional analysis and
started the local theory of Banach spaces. Olek once told
me that if it had been submitted somewhat later it might
not have been accepted because of the political situation
in the Middle East.
When meeting a colleague Olek would ask, “What is
new in mathematics?” If a student or junior person would
answer “nothing,” he had a particular way of saying “I see”
which instantly made you feel bad.
On Saturday evening December 12, 1981 I boarded an
overnight train in Vienna heading for Warsaw. The next
morning turned out to be beautiful with sun shining and
snow on the ground. As promised, Olek was at the train
station to pick me up. His first words were, “We have martial
law.” It took me some time to realize what it meant.
While still at the train station Olek showed me one of
many posters people could read telling them what was
allowed and what was forbidden. He did not lose his sense
of humor, translating a poster pointing to the edict “No
public performances” and saying, “This applies to you.”
At the time I occasionally performed magic.
I stayed at his place. He summarized the situation saying,
“Probably you have to stay longer which is good, so
we can do mathematics.” But it was clear that Olek was
worried. He would quietly fill the bathtub with water in
case the water supply would end. Meetings and gatherings
were not allowed, but seminars were, and a Russian
colleague and I were giving seminar talks. After the talks
Olek apologized, “I am sorry but people were not really
listening.”
Joe Diestel:
Olek was a very generous man. In 1976, Jerry Uhl and
I were putting the finishing touches on a book and Olek
visited Kent to give a colloquium talk. During his talk
he gave a proof that the disc algebra, which was known
to have a Schauder basis, did not have an unconditional
basis; more precisely, the disc algebra did not have local
unconditional structure (LUST, as Olek referred to the
property to make it more “interesting”) and so was not
even isomorphic to a Banach lattice. His proof used many
of the best results we were presenting in our book. He
told us he’d fashioned the proof just for us and agreed
we could use it in our text, if we so desired. We did and it
added much to our Notes and Remarks.
Stanislaw Szarek:
As a student at Warsaw University I took a seminar-type
class co-taught by Olek and Staszek Kwapien on sequences
and series in normed spaces. At the first meeting we were
given a list of topics to present and problems to solve.
Most of the problems were just hard exercises, but some
were true open problems. There was a lot of enthusiasm,
both on the side of the instructors and on the side of the
participants. I guess it was that seminar that attracted
me to functional analysis; before that, I was primarily
interested in mathematics that was directly relevant to
physics. One of the open problems led the following year
to my first paper on the best constants in the Khinchine
inequality. It was some time around then that Olek became
my official advisor. We met frequently on a one-to-one
basis and all those encounters were invaluable to my development
as a mathematician. On the one hand he was
incredibly generous with his time, knowledge, and ideas.
January 2017 Notices of the AMS 57

COMMUNICATION
Professor of
Mathematics
→ The Department of Mathematics
(www.math.ethz.ch) at ETH Zurich invites
applications for the above-mentioned
position.
→ Successful candidates have an outstanding
research record and a proven
ability to direct research work of high
quality. The new professor will be expected,
together with other members of
the Department, to teach undergraduate
level courses (German or English) and
graduate level courses (English) for students
of mathematics, natural sciences
and engineering. Willingness to participate
in collaborative work both within and
outside the school is expected.
→ Please apply online at
www.facultyaffairs.ethz.ch
→ Applications include a curriculum
vitae, a list of publications, a statement
of future research and teaching interests,
and a description of the three most
important achievements. The letter of
application should be addressed to the
President of ETH Zurich, Prof. Dr. Lino
Guzzella. The closing date for applications
is 28 February 2017. ETH Zurich is
an equal opportunity and family friendly
employer and is further responsive to the
needs of dual career couples. We specifically
encourage women to apply.
On the other hand, he was tough,
his legendary inquiries “What did
you prove this week?” being just
one example. With time, I got to
know him as a human being and
I think I could—with pride—call
myself his friend.
We close with Czeslaw Bessaga's
eulogy to Olek:
“What did
you prove
lately?”
Olek, what would you like to hear? What would you
want me to tell here? Most likely it can’t be of your enormous
scientific achievements nor of the respect that you
enjoyed in mathematical circles worldwide. You assessed
the value of your results soberly with no false modesty.
What interested you most were results of other mathematicians,
especially colleagues and pupils. Often you
started conversations with the question: “What did you
prove lately?” So you would surely be pleased if we, one
after another, tell about our latest achievements. There
will be a more suitable time for that.
Outside of mathematics you were interested in history
and literature. Perhaps not many of us who are gathered
here know that you were the initiator and creator of the
unprinted journal Acta Graphomanica Mathematica
[with its] prose and poetry, lots of humor and satire. …
I remember political satire—a famous series of zlomeks
authored by many mathematicians that promoted the action
of collecting scrap metal. I also remember epitaphs of
mathematicians living in Warsaw at the time. Finally, Olek,
I remember your elegant limericks, sonnets, and fraszkas,
somewhat in the spirit of Julian Tuwim.
Olek, I wish that, thanks to your papers and your disciples,
you inspire many future generations of mathematicians
helping in the development of Polish mathematics,
especially of Banach spaces.
Editor’s note: Notices regrets the delay in the publication
of this article.
Pelczynski and Czeslaw Bessaga.
Photo Credits
Photo of Nicole Tomczak-Jaegermann is courtesy of
W. Eryk Jaegermann.
All other article photos are courtesy of Joe Diestel.
58 Notices of the AMS Volume 64, Number 1

NEWS
Mathematics Opportunities
AMS-Simons Travel Grants
Program
Starting February 1, 2017, the AMS will begin accepting
applications for the AMS-Simons Travel Grants program,
with support from the Simons Foundation. Each grant
provides an early-career mathematician with US$2,000 per
year for two years to reimburse travel expenses related
to research. Applications will be accepted through www.
mathprograms.org. The deadline is March 31, 2017.
Simons Foundation
Collaboration Grants for
Mathematicians
—AMS announcement
The Simons Foundation invites applications for Collaboration
Grants for Mathematicians (US$8,400 per year for
five years). The application deadline is January 31, 2017.
See tinyurl.com/zvoqm5t.
—From a Simons Foundation announcement
*NSF Major Research
Instrumentation Program
The National Science Foundation (NSF) Major Research
Instrumentation (MRI) program helps institutions of
higher education or nonprofit organizations increase
access to shared scientific and engineering instruments
for research and research training. The deadline is
January 11, 2017; see www.nsf.gov/funding/pgm_summ.
jsp?pims_id=5260&org=MPS&sel_org=MPS&from=fund.
—From an NSF announcement
* The most up-to-date listing of NSF funding opportunities from
the Division of Mathematical Sciences can be found online at:
www.nsf.gov/dms and for the Directorate of Education and
Human Resources at www.nsf.gov/dir/index.jsp?org=ehr.
To receive periodic updates, subscribe to the DMSNEWS listserv by
following the directions at www.nsf.gov/mps/dms/about.jsp.
National Academies Research
Associateship Programs
The National Academies 2017 Postdoctoral and Senior
Research Associateship Programs provide opportunities
for both US and non-US nationals to research at more than
100 laboratories. Full-time associateships are awarded in
mathematics, chemistry, earth and atmospheric sciences,
engineering, applied sciences, life sciences, space sciences,
and physics. See sites.nationalacademies.org/PGA/
RAP/PGA_050491.
PIMS Education Prize
—From an NRC announcement
The Pacific Institute for the Mathematical Sciences (PIMS)
annually awards a prize to a member of the PIMS community
who has made a significant contribution to education
in the mathematical sciences. The deadline for nominations
is March 15, 2017; see www.pims.math.ca/pimsglance/prizes-awards.
—From a PIMS announcement
CAIMS/PIMS Early Career
Award
The Canadian Applied and Industrial Mathematics Society
(CAIMS) and the Pacific Institute for Mathematical Sciences
(PIMS) sponsor the Early Career Award in Applied
Mathematics to recognize exceptional research in applied
mathematics, interpreted broadly, by a researcher fewer
than ten years past earning a PhD. The nominee’s research
should have been conducted primarily in Canada or in
affiliation with a Canadian university. The deadline for
nominations is January 31, 2017; see www.pims.math.
ca/pims-glance/prizes-awards.
—From a PIMS announcement
60 Notices of the AMS Volume 64, Number 1

Mathematics Opportunities
Call for Applications for the
Fifth Heidelberg Laureate
Forum
NEWS
The Fifth Heidelberg Laureate Forum (HLF) will be held
September 24–29, 2017, bringing together winners of the
Abel Prize and the Fields Medal, both in mathematics, as
well as the Turing Award and the Nevanlinna Prize, both
in computer science. Young researchers from these fields
interested in attending should submit applications online
at application.heidelberg-laureate-forum.org
by February 14, 2017; see www.heidelberg-laureateforum.org/
for more information.
—From a Heidelberg Laureate
Forum Foundation announcement
Department of Mathematics
Founded in 1963, The Chinese University of Hong Kong (CUHK) is a forward-looking
comprehensive research university with a global vision and a mission to combine
tradition with modernity, and to bring together China and the West.
The Department of Mathematics in CUHK has developed a strong reputation in teaching
and research. Many faculty members are internationally renowned and are recipients
of prestigious awards and honors. The graduates are successful in both academia and
industry. The Department is highly ranked internationally. According to the latest
rankings, the Department is 39th in the Academic Ranking of World Universities, 27th
in the QS World University Rankings and 28th in the US News Rankings.
(1) Associate Professor / Assistant Professor
(Ref. 16000267) (Closing date: June 30, 2017)
Applications are invited for a substantiable-track faculty position at the Associate
Professor / Assistant Professor level. Candidates with strong evidence of outstanding
research accomplishments and promise in both research and teaching in Optimization
or related fields in Applied Mathematics are encouraged to apply.
Appointment will normally be made on contract basis for up to three years initially
commencing August 2017, which, subject to mutual agreement, may lead to longerterm
appointment or substantiation later.
(2) Research Assistant Professor
(Ref. 1600027V) (Closing date: June 30, 2017)
Applications are invited for a position of Research Assistant Professor in all areas of
Mathematics. Applicants should have a relevant PhD degree and good potential for
research and teaching.
Appointment will initially be made on contract basis for up to three years commencing
August 2017, renewable subject to mutual agreement.
For posts (1) and (2): The applications will be considered on a continuing basis but
candidates are encouraged to apply by January 31, 2017.
Application Procedure
The University only accepts and considers applications submitted online
for the posts above. For more information and to apply online, please visit
http://career.cuhk.edu.hk.
January 2017 Notices of the AMS 61

NEWS
Inside the AMS
Erd˝ os Memorial Lecture
The Erd˝ os Memorial Lecture is an annual invited address
named for the prolific mathematician Paul Erd˝ os (1913–
1996). The lectures are supported by a fund created by
Andrew Beal, a Dallas banker and mathematics enthusiast.
The Beal Prize Fund, now US$100,000, is being held by the
AMS until it is awarded for a correct solution to the Beal
Conjecture (see www.math.unt.edu/~mauldin/beal.
html). At Mr. Beal’s request, the interest from the fund is
used to support the Erd˝ os Memorial Lecture.
James Maynard of Magdalen College will present the
2017 Erd˝ os Memorial Lecture during the Spring Eastern
Sectional Meeting at Hunter College, City University of New
York, May 6–7, 2017. For more details, see www.ams.org/
meetings/lectures/meet-erdos-lect.
Deaths of AMS Members
—AMS announcement
Ichiro Satake, of Japan, died on October 10, 2014. Born
on December 25, 1927, he was a member of the Society
for 54 years.
John C. Moore, of Rochester, New York, died on January
1, 2016. Born on May 27, 1923, he was a member of
the Society for 66 years.
Jean J. Pedersen, of Santa Clara, California, died on
January 1, 2016. Born on September 17, 1934, he was a
member of the Society for 37 years.
Norman E. Sexauer, of Seal Beach, California, died
on January 7, 2016. Born on February 26, 1925, he was a
member of the Society for 61 years.
William Craig, professor, University of California,
Berkeley, died on January 13, 2016. Born on November
13, 1918, he was a member of the Society for 59 years.
Scott Smedinghoff, graduate student, Dartmouth
College, died on January 13, 2016. Born on June 15, 1987,
he was a member of the Society for 2 years.
E. H. Kronheimer, of the United Kingdom, died on
January 19, 2016. Born on February 11, 1928, he was a
member of the Society for 47 years.
Carl J. Sinke, of Kentwood, Michigan, died on January
20, 2016. Born on October 15, 1928, he was a member
of the Society for 64 years.
William H. Reid, of St. Johns, Florida, died on January
31, 2016. Born on September 10, 1926, he was a member
of the Society for 53 years.
Hans Heinrich Brungs, of Canada, died on February
4, 2016. Born on December 28, 1939, he was a member of
the Society for 31 years.
Clarence M. Ablow, of Tustin, California, died on
February 9, 2016. Born on November 6, 1919, he was a
member of the Society for 74 years.
Salvatore Anastasio, of St. James City, Florida, died
on February 11, 2016. Born on March 12, 1932, he was a
member of the Society for 52 years.
James F. Jakobsen, of Iowa City, Iowa, died on February
13, 2016. Born on May 25, 1927, he was a member of the
Society for 62 years.
Mark Alan Cooper, of Clifton, New Jersey, died on February
21, 2016. Born on March 8, 1950, he was a member
of the Society for 39 years.
Uwe R. Helmke, professor, University of Wurzburg,
died on March 1, 2016. Born on April 26, 1952, he was a
member of the Society for 20 years.
Robert Silverman, of Yellow Springs, Ohio, died on
March 5, 2016. Born on October 23, 1928, he was a member
of the Society for 57 years.
Verena Huber-Dyson, of Bellingham, Washington,
died on March 12, 2016. Born on May 6, 1923, she was a
member of the Society for 66 years.
Lloyd S. Shapley, professor, University of California
Los Angeles, died on March 12, 2016. Born on June 2, 1923,
he was a member of the Society for 66 years.
Marj Enneking, of Portland, Oregon, died on March
13, 2016. Born on June 21, 1941, she was a member of
the Society for 50 years.
62 Notices of the AMS Volume 64, Number 1

To subscribe to email notification of new AMS publications,
please go to www.ams.org/bookstore-email.
Algebra and Algebraic
Geometry
Lectures on Chevalley
Groups
Robert Steinberg
Robert Steinberg’s Lectures on Chevalley
Groups were delivered and written during
the author’s sabbatical visit to Yale
University in the 1967–1968 academic
year. The work presents the status of
the theory of Chevalley groups as it was
in the mid-1960s. Much of this material
was instrumental in many areas of
mathematics, in particular in the theory of algebraic groups and in
the subsequent classification of finite groups. This posthumous
edition incorporates additions and corrections prepared by the
author during his retirement, including a new introductory
chapter. A bibliography and editorial notes have also been added.
This is a great unsurpassed introduction to the subject of Chevalley
groups that influenced generations of mathematicians. I would
recommend it to anybody whose interests include group theory.
—Efim Zelmanov, University of California, San Diego
Robert Steinberg’s lectures on Chevalley groups were given at Yale
University in 1967. The notes for the lectures contain a wonderful
exposition of the work of Chevalley, as well as important additions
to that work due to Steinberg himself. The theory of Chevalley
groups is of central importance not only for group theory, but
also for number theory and theoretical physics, and is as relevant
today as it was in 1967. The publication of these lecture notes in
book form is a very welcome addition to the literature.
—George Lusztig, Massachusetts Institute of Technology
Robert Steinberg gave a course at Yale University in 1967 and the
mimeographed notes of that course have been read by essentially
anyone interested in Chevalley groups. In this course, Steinberg
presents the basic constructions of the Chevalley groups over
arbitrary fields. He also presents fundamental material about
generators and relations for these groups and automorphism
groups. Twisted variations on the Chevalley groups are also
introduced. There are several chapters on the representation
theory of the Chevalley groups (over an arbitrary field) and for
many of the finite twisted groups. Even 50 years later, this book is
still one of the best introductions to the theory of Chevalley groups
and should be read by anyone interested in the field.
—Robert Guralnick, University of Southern California
A Russian translation of this lecture course by Robert Steinberg
was published in Russia more than 40 years ago, but for some
mysterious reason has never been published in the original
language. This book is very dear to me. It is not only an important
advance in the theory of algebraic groups, but it has also played a
key role in more recent developments of the theory of Kac-Moody
groups. The very different approaches, one by Tits and another
by Peterson and myself, borrowed heavily from this remarkable
book.
—Victor Kac, Massachusetts Institute of Technology
Contents: Introduction; A basis for L; A basis for U; The
Chevalley groups; Simplicity of G; Chevalley groups and algebraic
groups; Generators and relations; Central extensions; Variants
of the Bruhat lemma; The orders of the finite Chevalley groups;
Isomorphisms and automorphisms; Some twisted groups;
Representations; Representations continued; Representations
completed; Appendix on finite reflection groups; Bibliography;
Index.
University Lecture Series, Volume 66
January 2017, 160 pages, Softcover, ISBN: 978-1-4704-3105-1,
LC 2016042277, 2010 Mathematics Subject Classification: 20G15;
14Lxx, AMS members US$28, List US$35, Order code ULECT/66
January 2017 Notices of the AMS 63

Analysis
Recent Progress on
Operator Theory and
Approximation in
Spaces of Analytic
Functions
Catherine Bénéteau, University
of South Florida, Tampa, FL,
Alberto A. Condori, Florida Gulf
Coast University, Fort Myers,
FL, Constanze Liaw, Baylor
University, Waco, TX, William T.
Ross, University of Richmond,
VA, and Alan A. Sola, University
of South Florida, Tampa, FL,
Editors
This volume contains the Proceedings of the Conference on
Completeness Problems, Carleson Measures, and Spaces of
Analytic Functions, held from June 29–July 3, 2015, at the Institut
Mittag-Leffler, Djursholm, Sweden.
The conference brought together experienced researchers and
promising young mathematicians from many countries to
discuss recent progress made in function theory, model spaces,
completeness problems, and Carleson measures.
This volume contains articles covering cutting-edge research
questions, as well as longer survey papers and a report on the
problem session that contains a collection of attractive open
problems in complex and harmonic analysis.
Contents: K. Bickel and C. Liaw, Properties of vector-valued
submodules on the bidisk; A. Bourhim and J. Mashreghi,
Composition operators on the Hardy–Hilbert space H 2 and
model spaces K Θ ; I. Chalendar, E. Fricain, and D. Timotin, A
survey of some recent results on truncated Toeplitz operators;
M. Fleeman and D. Khavinson, Approximating z in the Bergman
space; S. R. Garcia, J. Mashreghi, and W. T. Ross, Real complex
functions; P. Gorkin and B. D. Wick, Thin interpolating sequences;
A. Hartmann and M. Mitkovski, Kernels of Toeplitz operators;
E. Saksman and K. Seip, Some open questions in analysis for
Dirichlet series; D. Seco, Some problems on optimal approximants;
C. Bénéteau, A. A. Condori, C. Liaw, W. T. Ross, and A. A. Sola,
Some open problems in complex and harmonic analysis: Report
on problem session held during the conference Completeness
problems, Carleson measures, and space of analytic functions.
Contemporary Mathematics, Volume 679
January 2017, 217 pages, Softcover, ISBN: 978-1-4704-2305-6,
LC 2016023124, 2010 Mathematics Subject Classification: 11M41,
30H05, 30H20, 35P10, 47A16, 47B32, AMS members US$86.40,
List US$108, Order code CONM/679
Geometry and Topology
Physics and
Mathematics of Link
Homology
Sergei Gukov, California
Institute of Technology,
Pasadena, CA, Mikhail
Khovanov, Columbia University,
New York, NY, and Johannes
Walcher, Ruprecht-Karls-
Universität Heidelberg, Germany,
Editors
Throughout recent history, the theory of knot invariants has been
a fascinating melting pot of ideas and scientific cultures, blending
mathematics and physics, geometry, topology and algebra, gauge
theory, and quantum gravity.
The 2013 Séminaire de Mathématiques Supérieures in Montréal
presented an opportunity for the next generation of scientists
to learn in one place about the various perspectives on knot
homology, from the mathematical background to the most recent
developments, and provided an access point to the relevant parts
of theoretical physics as well.
This volume presents a cross-section of topics covered at that
summer school and will be a valuable resource for graduate
students and researchers wishing to learn about this rapidly
growing field.
This item will also be of interest to those working in mathematical
physics.
This book is co-published with the Centre de Recherches
Mathématiques.
Contents: R. Pichai and V. K. Singh, Chern-Simons theory and knot
invariants; B. Webster, Tensor product algebras, Grassmannians
and Khovanov homology; S. Gukov and I. Saberi, Lectures on knot
homology and quantum curves; C. Manolescu, An introduction to
knot Floer homology; S. Nawata and A. Oblomkov, Lectures on
knot homology.
Contemporary Mathematics, Volume 680
January 2017, 177 pages, Softcover, ISBN: 978-1-4704-1459-7,
LC 2016027525, 2010 Mathematics Subject Classification: 17B37,
57M27, 57R58, 81T45, 81T30, AMS members US$86.40, List
US$108, Order code CONM/680
64 Notices of the AMS Volume 64, Number 1

New AMS-Distributed
Publications
Algebra and Algebraic
Geometry
On the Derived
Category of 1-Motives
Luca Barbieri-Viale, Università
degli Studi di Milano, Italy,
and Bruno Kahn, Institut de
Mathématiques de Jussieu-Paris
Rive Gauche, France
The authors embed the derived category
of Deligne 1-motives over a perfect field
into the étale version of Voevodsky’s
triangulated category of geometric motives after inverting
the exponential characteristic. They then show that this full
embedding “almost” has a left adjoint LAlb. Applying LAlb to
the motive of a variety, the authors get a bounded complex
of 1-motives that they compute fully for smooth varieties and
partly for singular varieties. Among applications, the authors
give motivic proofs of Roitman type theorems and new cases of
Deligne’s conjectures on 1-motives.
A publication of the Société Mathématique de France, Marseilles
(SMF), distributed by the AMS in the U.S., Canada, and Mexico.
Orders from other countries should be sent to the SMF. Members
of the SMF receive a 30% discount from list.
Astérisque, Number 381
September 2016, 254 pages, Softcover, ISBN: 978-2-85629-837-4,
2010 Mathematics Subject Classification: 19E15, 14C15, 14F20,
14C30, 18E30, AMS members US$60, List US$75, Order code
AST/381
Minimal Models and
Extremal Rays
(Kyoto, 2011)
János Kollár, Princeton
University, NJ, Osamu Fujino,
Osaka University, Japan, Shigeru
Mukai, Kyoto University, Japan,
and Noboru Nakayama, Kyoto
University, Japan, Editors
Since the appearance of extremal rays and the minimal model
program in the early 1980s, we have seen the tremendous
development of algebraic geometry. With this in mind, the
conference on Minimal Models and Extremal Ray was held at the
Research Institute for Mathematical Sciences (RIMS) at Kyoto
University in June 2011. The purpose of the conference was to
review the past, examine the present, and enjoy discussing the
future.
This volume contains the proceedings of this conference and
consists of one survey article on the mathematical work of
Shigefumi Mori, who turned sixty in 2011, and thirteen research
papers presented by the authors.
Published for the Mathematical Society of Japan by Kinokuniya,
Tokyo, and distributed worldwide, except in Japan, by the AMS.
Advanced Studies in Pure Mathematics, Volume 70
September 2016, 420 pages, Hardcover, ISBN: 978-4-86497-036-
5, 2010 Mathematics Subject Classification: 14-06; 14E30, 14B07,
14D05, 14E07, 14E15, 14F17, 14F18, 14J17, 14J28, 14J32, 14J45,
53D05, AMS members US$121.60, List US$152, Order code
ASPM/70
Analysis
Dynamics Done with
Your Bare Hands
Lecture Notes by Diana
Davis, Bryce Weaver,
Roland K. W. Roeder, and
Pablo Lessa
Françoise Dal’Bo, Université
de Rennnes I, France, François
Ledrappier, University of Notre
Dame, IN, and Amie Wilkinson,
University of Chicago, IL, Editors
This book arose from four lectures given at the Undergraduate
Summer School of the Thematic Program Dynamics and
Boundaries, held at the University of Notre Dame. It is intended
to introduce (under)graduate students to the field of dynamical
systems by emphasizing elementary examples, exercises, and bare
hands constructions.
The lecture by Diana Davis is devoted to billiard flows on polygons,
a simple-sounding class of continuous time dynamical system for
which many problems remain open. Bryce Weaver focuses on the
dynamics of a 2 × 2 matrix acting on the flat torus. This example
introduced by Vladimir Arnold illustrates the wide class of
uniformly hyperbolic dynamical systems, including the geodesic
flow for negatively curved, compact manifolds. Roland Roeder
considers a dynamical system on the complex plane governed by
a quadratic map with a complex parameter. These maps exhibit
complicated dynamics related to the Mandelbrot set defined as
the set of parameters for which the orbit remains bounded. Pablo
Lessa deals with a type of non-deterministic dynamical system: a
simple walk on an infinite graph, obtained by starting at a vertex
and choosing a random neighbor at each step. The central question
concerns the recurrence property. When the graph is a Cayley
graph of a group, the behavior of the walk is deeply related to
algebraic properties of the group.
January 2017 Notices of the AMS 65

A publication of the European Mathematical Society (EMS).
Distributed within the Americas by the American Mathematical
Society.
EMS Series of Lectures in Mathematics, Volume 26
November 2016, 214 pages, Softcover, ISBN: 978-3-03719-168-2,
2010 Mathematics Subject Classification: 37Axx, 37Bxx, 37Dxx,
37Fxx, 37Hxx, 53Axx, AMS members US$35.20, List US$44, Order
code EMSSERLEC/26
Geometry and Topology
Geometry, Analysis
and Dynamics on
sub-Riemannian
Manifolds: Volume II
Davide Barilari, Université
Paris-Diderot, France, Ugo
Boscain, École Polytechnique,
Palaiseau, France, and Mario
Sigalotti, École Polytechnique,
Palaiseau, France, Editors
Sub-Riemannian manifolds model media with constrained
dynamics: motion at any point is allowed only along a limited
set of directions, which are prescribed by the physical problem.
From the theoretical point of view, sub-Riemannian geometry is
the geometry underlying the theory of hypoelliptic operators and
degenerate diffusions on manifolds.
In the last twenty years, sub-Riemannian geometry has emerged
as an independent research domain, with extremely rich
motivations and ramifications in several parts of pure and applied
mathematics, such as geometric analysis, geometric measure
theory, stochastic calculus and evolution equations together with
applications in mechanics, optimal control and biology.
The aim of the lectures collected here is to present sub-Riemannian
structures for the use of both researchers and graduate students.
This item will also be of interest to those working in differential
equations.
A publication of the European Mathematical Society (EMS).
Distributed within the Americas by the American Mathematical
Society.
EMS Series of Lectures in Mathematics, Volume 25
October 2016, 307 pages, Softcover, ISBN: 978-3-03719-163-7,
2010 Mathematics Subject Classification: 53C17, 35H10, 60H30,
49J15, AMS members US$46.40, List US$58, Order code
EMSSERLEC/25
Lectures on Quantum
Topology in
Dimension Three
Thang T. Q. Lê, Georgia Institute
of Technology, Atlanta, Georgia,
Christine Lescop, Université
Grenoble Alpes, France, Robert
Lipshitz, Columbia University,
New York, NY, and Paul Turner,
Université de Genève, Geneva,
Switzerland
This monograph contains three lecture series from the SMF
school Geometric and Quantum Topology in Dimension 3, which
was held at CIRM in June 2014. These lectures present recent
progress on the study of 3-manifold and link invariants. Thang
Lê describes the state of the art about the AJ conjecture, which
relates generalizations of the Jones polynomial to the Cooper,
Culler, Gillet, Long and Shalen A-polynomial, which is defined
from SL 2 (C)-representation spaces of link exterior fundamental
groups.
In 1999, Khovanov defined a homology theory for knots of R 3
whose Euler characteristic is the Jones polynomial. Paul Turner
presents the latest developments and the applications of this
categorification of the Jones polynomial in a useful guide of the
literature around this extensively studied topic. Robert Lipshitz
presents the famous Osváth Szábo Heegaard Floer homology
theories together with efficient sketches of proofs of some of
their spectacular applications. These lectures are introduced by
a partial survey of the history of these invariants, written by
Christine Lescop.
A publication of the Société Mathématique de France, Marseilles
(SMF), distributed by the AMS in the U.S., Canada, and Mexico.
Orders from other countries should be sent to the SMF. Members
of the SMF receive a 30% discount from list.
Panoramas et Synthèses, Number 48
September 2016, 174 pages, Softcover, ISBN: 978-2-85629-842-8,
2010 Mathematics Subject Classification: 57M27, 57M25, 57N10,
AMS members US$41.60, List US$52, Order code PASY/48
66 Notices of the AMS Volume 64, Number 1

Number Theory
La Conjecture Locale
de Gross-Prasad pour
les Représentations
Tempérées des
Groupes Unitaires
Raphaël Beuzart-Plessis,
Université d’Aix-Marseille, France
A note to readers: This book is in French.
This volume represents a straight continuation of Waldspurger’s
recent work that deals with special orthogonal groups.
A publication of the Société Mathématique de France, Marseilles
(SMF), distributed by the AMS in the U.S., Canada, and Mexico.
Orders from other countries should be sent to the SMF. Members
of the SMF receive a 30% discount from list.
Mémoires de la Société Mathématique de France, Number 149
September 2016, 164 pages, Softcover, ISBN: 978-2-85629-841-1,
2010 Mathematics Subject Classification: 22E50, 11F85, 20G05,
AMS members US$53.60, List US$67, Order code SMFMEM/149
Cloth $29.95
Cloth $29.95
Fashion, Faith, and Fantasy
in the New Physics of
the Universe
Roger Penrose
“ An extremely original, rich, and thoughtful
survey of today’s most fashionable attempts
to decipher the cosmos on its smallest and
largest scales.”
—Mario Livio, Science
The Joy of SET
The Many Mathematical
Dimensions of a Seemingly
Simple Card Game
Liz McMahon, Gary Gordon,
Hannah Gordon & Rebecca Gordon
“ SET is, arguably, the most popular of all
commercially sold mathematical games.
This is the only book that gives a solid
mathematical treatment of this game.”
— Arthur Benjamin, author of The Magic
of Math
Paper $27.95
Cloth $75.00
The Real Analysis Lifesaver
All the Tools You Need to
Understand Proofs
Raffi Grinberg
“ This book is a great resource that every
real analysis student should have. Grinberg
writes like a professor would speak to a
student during office hours: free of jargon,
with a sense of humor, yet still in an
authoritative and informative manner.”
— Oscar E. Fernandez, author of
Everyday Calculus
A Princeton Lifesaver Study Guide
Enlightening Symbols
A Short History of Mathematical
Notation and Its Hidden Powers
Joseph Mazur
“ A nuanced, intelligently framed chronicle
packed with nuggets. . . . In a word:
enlightening.”
—George Szpiro, Nature
Paper $19.95
See our E-Books at press.princeton.edu
January 2017 Notices of the AMS 67
DO NOT PRINT THIS INFORMATION AMS NOTICES JANUARY 2017 17-073

Classified Advertisements
Positions available, items for sale, services available, and more
CONNECTICUT
UNIVERSITY OF CONNECTICUT
Department of Mathematics
Assistant, Associate, or Full Professor
The Department of Mathematics at the
University of Connecticut, Storrs, invites
applications for full-time, 9-month tenuretrack
faculty positions at the rank of
Assistant, Associate, or Full Professor in
Mathematics beginning in fall 2017. We
are seeking exceptionally well-qualified
individuals with outstanding research
programs. The successful candidate will
be expected to teach mathematics courses
at all levels and to have a vigorous externally
funded research program.
UConn has grown rapidly in the past
decade to become one of the nation's Top
20 public universities, with an ambitious
goal, at this transformational time in its
history, to join the ranks of the greatest
universities in the world. As one of
the University's emphasized STEM programs,
supported by the $1.7B Next Generation
Connecticut (nextgenct.uconn.
edu) investment, the math department
enjoys an active and dynamic academic
environment. The department currently
has 43 research faculty members with
diverse research interests (including financial
mathematics and actuarial science,
algebra and number theory, analysis,
applied math, geometry and topology,
mathematical logic, math education, numerical
analysis, partial differential equations,
and probability) and a strong record
of external funding. Faculty members in
the department participate in a range of
interdisciplinary projects with Physics,
Philosophy, Life Sciences, Statistics, and
with the Neag School of Education. The
department has moved into a new building
in fall 2016.
The successful candidates for these
positions will be expected to contribute
to research and scholarship through extramural
funding (in disciplines where
applicable), high quality publications,
impact as measured through citations,
performances and exhibits (in disciplines
where applicable), and national recognition
as through honorific awards. In the
area of teaching, the candidate will share a
deep commitment to effective instruction
at the undergraduate and graduate levels,
development of innovative courses and
mentoring of students in research, outreach
and professional development. Successful
candidates will also be expected
to broaden participation among members
of under-represented groups; demonstrate
through their research, teaching,
and/or public engagement the richness
of diversity in the learning experience;
integrate multicultural experiences into
instructional methods and research tools;
and provide leadership in developing
pedagogical techniques designed to meet
the needs of diverse learning styles and
intellectual interests.
Minimum Qualifications: A PhD or an
equivalent foreign degree in mathematics
or a closely related area by August 22,
2017, demonstrated evidence of excellent
teaching and outstanding research; and a
deep commitment to promoting diversity
through academic and research programs.
Equivalent foreign degrees are acceptable.
Preferred Qualifications: An outstanding
research program in an area that
complements the research activity in
the department; a record of attracting
external funding; a commitment to
effective teaching at the graduate and undergraduate
levels including integrating
Suggested uses for classified advertising are positions available, books or lecture notes for sale, books being sought, exchange or rental of houses,
and typing services. The publisher reserves the right to reject any advertising not in keeping with the publication's standards. Acceptance shall not be
construed as approval of the accuracy or the legality of any advertising.
The 2016 rate is $3.50 per word with a minimum two-line headline. No discounts for multiple ads or the same ad in consecutive issues. For an additional
$10 charge, announcements can be placed anonymously. Correspondence will be forwarded.
Advertisements in the “Positions Available” classified section will be set with a minimum one-line headline, consisting of the institution name above
body copy, unless additional headline copy is specified by the advertiser. Headlines will be centered in boldface at no extra charge. Ads will appear in the
language in which they are submitted.
There are no member discounts for classified ads. Dictation over the telephone will not be accepted for classified ads.
Upcoming deadlines for classified advertising are as follows: February 2017—December 2, 2016; March 2017—January 2, 2017; April 2017—February 3,
2017; May 2017—March 9, 2017; June/July 2017—May 9, 2017; August 2017—June 6, 2017.
US laws prohibit discrimination in employment on the basis of color, age, sex, race, religion, or national origin. “Positions Available” advertisements
from institutions outside the US cannot be published unless they are accompanied by a statement that the institution does not discriminate on these
grounds whether or not it is subject to US laws. Details and specific wording may be found on page 1373 (vol. 44).
Situations wanted advertisements from involuntarily unemployed mathematicians are accepted under certain conditions for free publication. Call
toll-free 800-321-4AMS (321-4267) in the US and Canada or 401-455-4084 worldwide for further information.
Submission: Promotions Department, AMS, P.O. Box 6248, Providence, Rhode Island 02904; or via fax: 401-331-3842; or send email to classads@ams.org.
AMS location for express delivery packages is 201 Charles Street, Providence, Rhode Island 02904. Advertisers will be billed upon publication.
68 Notices of the AMS Volume 64, Number 1

Classified Advertisements
technology into instruction, such as online
instruction; and the ability to contribute
through research, teaching, and/or public
engagement to the diversity and excellence
of the learning experience.
Appointment Terms: These are fulltime,
9-month, tenure-track positions
with an anticipated start date of August
23, 2017. The successful candidate’s
academic appointment will be at the
Storrs campus. Faculty may also be asked
to teach at one of UConn’s regional campuses
as part of their ordinary workload.
Rank and salary will be commensurate
with qualifications and experience.
To Apply: Submit a cover letter, curriculum
vitae, teaching statement (including
teaching philosophy, teaching experience,
commitment to effective learning,
concepts for new course development,
etc.), research and scholarship statement
(innovative concepts that will form the
basis of academic career, experience in
proposal development, mentorship of
graduate students, etc.), commitment to
diversity statement (including broadening
participation, integrating multicultural
experiences in instruction and research
and pedagogical techniques to meet the
needs of diverse learning styles, etc.); and
five letters of reference, one of which addresses
the applicant’s teaching online at
www.mathjobs.org.jobs.
Evaluation of applications will begin
on November 21, 2016. Employment of
the successful candidate will be contingent
upon the successful completion of
a pre-employment criminal background
check. Questions or requests for further
information should be sent to the Hiring
Committee at mathhiring@uconn.edu.
All employees are subject to adherence
to the State Code of Ethics which may be
found at www.ct.gov/ethics/site/
default.asp.
The University of Connecticut is committed
to building and supporting a multicultural
and diverse community of students,
faculty and staff. The diversity of
students, faculty and staff continues to
increase, as does the number of honors
students, valedictorians and salutatorians
who consistently make UConn their
top choice. More than 100 research centers
and institutes serve the University’s
teaching, research, diversity, and outreach
missions, leading to UConn’s ranking as
one of the nation’s top research universities.
UConn’s faculty and staff are the
critical link to fostering and expanding
our vibrant, multicultural and diverse
University community. As an Affirmative
Action/Equal Employment Opportunity
employer, UConn encourages applications
from women, veterans, people with
disabilities and members of traditionally
underrepresented populations.
000059
UNIVERSITY OF CONNECTICUT
Department of Mathematics
Assistant Professor in Residence
The Department of Mathematics at the
University of Connecticut invites applications
for positions at the rank of Assistant
Professor in Residence beginning in fall
2017. The number of positions is subject
to budgetary constraints.
The University of Connecticut (UConn)
is in the midst of a transformational
period of growth supported by the
$1.7B Next Generation Connecticut
(nextgenct.uconn.edu) and the $1B
Bioscience Connecticut (biosciencect.
uchc.edu) investments and a bold new
Academic Plan: Path to Excellence (issuu.
com/uconnprovost/docs/academicplan-single-hi-optimized
1). We are
pleased to continue these investments by
inviting applications for faculty positions
in the Department of Mathematics at the
rank of Assistant Professor in Residence.
The Mathematics Department has active
programs in various areas of mathematical
research including mathematics
education. The education group works
on issues across the K–20 spectrum, with
particular emphasis on mathematics content,
and on applications of mathematics
education research to instruction in the
department. This group works closely
with the Center for Research in Mathematics
Education, based in the Neag School of
Education. Successful candidates who are
interested in mathematics education will
have an opportunity to work on writing
and implementing grants within these
units.
These positions are open only to candidates
who have received a PhD in mathematics,
and are suitable for candidates
interested in a career at UConn with
an emphasis on teaching excellence. In
particular, the committee will be looking
within the applications for specific
evidence of outstanding teaching and experience
with educational technology and
interactive technological teaching tools.
Applicants with an interest in mathematics
education are strongly encouraged to
apply.
Minimum qualifications include: A PhD
in mathematics, a record of outstanding
teaching, and an interest in mathematics
education. Equivalent foreign degrees are
acceptable.
Preferred qualifications include: Experience
with educational technologies,
such as online homework systems, message
boards, videos, smart boards, or
classroom personal response systems
(“clickers”); experience teaching large lectures;
commitment to effective teaching,
the ability to contribute through research,
teaching, and/or public engagement to the
diversity and excellence of the learning
experience.
Appointment Terms: These are fulltime,
9-month, non-tenure track positions
which may lead to long-term multi-year
contracts. The teaching load for these
positions are approximately six courses
per year. These positions have an anticipated
start date of August 23, 2017.
The successful candidate’s academic appointment
will be at the Storrs campus.
Faculty may also be asked to teach at one
of UConn’s regional campuses as part of
their workload. Rank and salary will be
commensurate with qualifications and
experience.
To Apply: Submit a cover letter, curriculum
vitae, teaching statement (including
teaching philosophy, teaching experience,
commitment to effective learning,
concepts for new course development,
etc.), a commitment to diversity statement
(including broadening participation,
integrating multicultural experiences in
instruction and research and pedagogical
techniques to meet the needs of diverse
learning styles, etc.); and three letters of
reference, at least two of which address
the applicant’s teaching online at www.
mathjobs.org.jobs.
The review of applications will begin on
November 21, 2016. Employment of the
successful candidate will be contingent
upon the successful completion of a preemployment
criminal background check.
Questions or requests for further information
should be sent to the Hiring Committee
at vaphiring@math.uconn.edu.
All employees are subject to adherence
to the State Code of Ethics which may be
found at www.ct.gov/ethics/site/
default.asp.
The University of Connecticut is committed
to building and supporting a multicultural
and diverse community of students,
faculty and staff. The diversity of
students, faculty and staff continues to
increase, as does the number of honors
students, valedictorians and salutatorians
who consistently make UConn their
top choice. More than 100 research centers
and institutes serve the University’s
teaching, research, diversity, and outreach
missions, leading to UConn’s ranking as
one of the nation’s top research universities.
UConn’s faculty and staff are the
critical link to fostering and expanding
our vibrant, multicultural and diverse
University community. As an Affirmative
Action/Equal Employment Opportunity
employer, UConn encourages applications
from women, veterans, people with
disabilities and members of traditionally
underrepresented populations.
MAINE
000058
Bowdoin College
Tenure-Track, Assistant Professor
Tenure-track Assistant Professor position
starting fall 2017. Preference given
to applicants in the fields of number
theory or ergodic theory and theoretical
dynamics, areas which complement
the research interests of our faculty. We
January 2017 Notices of the AMS 69

Classified Advertisements
are particularly interested in mathematicians
whose research areas include both
theoretical and computational aspects.
Teaching two courses per semester, PhD
preferred, advanced ABDs considered.
Visit www.mathjobs.org to apply. Review
begins 12/7/16 and will continue
until position is filled.
Bowdoin College is committed to equality
and is an equal opportunity employer.
For a full description of the position and
further information about the College, see
www.bowdoin.edu.
MICHIGAN
Michigan State University
Department of Mathematics
000001
Michigan State University has a tenuresystem
faculty position to begin in the fall
2017 for the Actuarial Science program.
The search seeks candidates at the rank
of Assistant Professor, but outstanding
candidates at higher ranks may be considered.
Candidates must have a PhD in
mathematics or statistics with published
research directly related to actuarial science,
risk analysis, or financial mathematics.
Associate status with the Society of
Actuaries, the Casualty Actuarial Society,
or similarly recognized actuarial professional
association is desirable. The
successful candidate will be appointed
either in the Department of Mathematics,
or in the Department of Statistics and
Probability, or jointly between the two
departments.
Applications should include curriculum
vitae, research statement, teaching statement,
and should arrange for at least 4
letters of recommendation to be sent by
the letter writers through www.mathjobs.
org, one of which must specifically address
the applicant's teaching ability.
NORTH CAROLINA
Statistical & Applied Mathematical
Sciences Institute (SAMSI)
Director
000002
SAMSI is seeking its next Director, to
begin the position no later than July 1,
2018. Candidates with vision, energy,
and experience are encouraged to apply.
The appointment will be coincident with
appointment as a tenured faculty member
at one of the SAMSI partner universities:
Duke University, North Carolina State
University, or the University of North
Carolina–Chapel Hill.
The Director has primary responsibility
for the scientific leadership of SAMSI
and for the administrative and financial
functions required to realize the scientific
vision. They will be a scholar with
an international reputation of research in
statistics, applied mathematics or a
closely related field. SAMSI has a strong
record of interdisciplinary research covering
a wide variety of biological, physical
and social sciences, and is seeking to
expand actively in the fields of computing
and data science. In addition, the Director
is expected to have experience in university
or departmental administration, and a
willingness to provide leadership in other
areas of importance to SAMSI including
fundraising, education and outreach, and
diversity.
SAMSI is a mathematical sciences institute
whose primary source of funding
is the National Science Foundation. Dayto-day
management is in the hands of a
Directorate consisting of the Director, the
Deputy Director, two Associate Directors,
and an Operations Director. Financial and
personnel management of the institute are
overseen by a Governing Board chaired
by Professor Robert Calderbank (Duke),
including representatives of all three partner
universities as well as the American
Statistical Association and the Society for
Industrial and Applied Mathematics. The
selection of research programs is overseen
by a National Advisory Committee
consisting of leading national researchers
in statistics, applied mathematics and
disciplinary sciences. The Director has
ultimate responsibility for all the financial
and personnel decisions of the Institute,
for liaison with the partner universities
and the National Science Foundation, for
working with the Operations Director on
management of the staff and the facilities,
and for long-term planning including
fundraising. The Director also works
closely with the Deputy and Associate
Directors to provide ongoing oversight
of SAMSI research programs and of the
institute’s education, outreach and diversity
activities.
SAMSI is located in Research Triangle
Park, NC. The region is rich in terms
of statistical and applied mathematical
expertise, and in interdisciplinary scientists
which are essential to many SAMSI
programs.
Candidates are asked to send a CV and
cover letter to directorsearch@samsi.
info. Applications will receive fullest
consideration if received by January 1,
2017, and applications will remain open
until the position is filled.
Search Committee: James Berger (chair,
Duke University), Mihai Anitescu (Argonne
National Laboratory), Robert Calderbank
(Duke University), Marie Davidian (North
Carolina State University), M. Gregory
Forest (University of North Carolina, Chapel
Hill), Susan A. Murphy (University
of Michigan), Javier Rojo (University of
Nevada, Reno), Richard Smith (University
of North Carolina, Chapel Hill), Michael
Stein (University of Chicago), Margaret H.
Wright (Courant Institute of Mathematical
Sciences), Linda J. Young (National Agricultural
Statistics Service).
SAMSI is an equal opportunity/affirmative
action employer.
000004
PENNSYLVANIA
Penn State University
Department of Mathematics
The Department of Mathematics is seeking
exceptional applicants for one tenure
or tenure-track faculty position specializing
in big data research with mathematics
background in one or more areas of highdimensional
geometry, algebraic geometry,
algebraic topology, computational
geometry, topological data analysis, representation
theory and noncommutative
harmonic analysis, homological algebra,
randomized numerical linear algebra,
recurrent neural networks, and multiple
areas in machine learning including deep
learning. A PhD is required. Applicants
must complete the Penn State application
at https://psu.jobs/job/67556
and must submit an application through
MathJobs.Org (https://www.mathjobs.
org/jobs) with the following materials in
order for the application to be complete:
(1) at least three reference letters, one of
which should address in detail the candidate's
abilities as a teacher, (2) Curriculum
Vitae, (3) Publication List, (4) Research
Statement, and (5) Teaching Statement. We
encourage applications from individuals
of diverse backgrounds. Review of applications
will begin January 15, 2017 and
continue until the position is filled.
CAMPUS SECURITY CRIME STATISTICS:
For more about safety at Penn State, and
to review the Annual Security Report
which contains information about crime
statistics and other safety and security
matters, please go to www.police.psu.
edu/clery/, which will also provide you
with detail on how to request a hard copy
of the Annual Security Report.
Penn State is an equal opportunity, affirmative
action employer, and is committed
to providing employment opportunities
to all qualified applicants without regard
to race, color, religion, age, sex, sexual
orientation, gender identity, national origin,
disability or protected veteran status.
000003
70 Notices of the AMS Volume 64, Number 1

contains new announcements of worldwide meetings
and conferences of interest to the mathematical public,
including ad hoc, local, or regional meetings, and meetings
and symposia devoted to specialized topics, as well as announcements
of regularly scheduled meetings of national or
international mathematical organizations. New announcements
only are published in the print Mathematics Calendar
featured in each Notices issue.
will be published in the Notices if it contains
a call for papers and specifies the place, date, subject (when
applicable). A second announcement will be published only
if there are changes or necessary additional information. Asterisks
(*) mark those announcements containing revised
information.
print announcements of meetings and conferences
carry only the date, title and location of the
event.
of the Mathematics Calendar is available
at: www.ams.org/meetings/calendar/mathcal
to the Mathematics Calendar should be done
online via: www.ams.org/cgi-bin/mathcal/mathcalsubmit.pl
or difficulties may be directed to mathcal@ams.
org.
22 – 23
Department of Mathematics, Gauhati University,
Guwahati, Assam, India.
sites.google.com/site/ncamsgu2016
5 – 9
Dayanand Science College, Latur, India.
dsclatur.org/icmaa2017
8 – 9
Ferdowsi University of Mashhad, Iran.
ota3.um.ac.ir/index.php?&newlang=eng
17 – 19
University of South Alabama, Mobile, Alabama.
www.southalabama.edu/colleges/artsandsci/
mathstat/srac/index.html
31 – April 2
Amherst College, Amherst, Massachusetts.
www.ustars.org
3 – 6
University of Zagreb, Zagreb, Croatia.
www.fer.unizg.hr/mampit/events/workshop
8 – 8
North Dakota State University, Fargo, North Dakota.
https://www.ndsu.edu/pubweb/~isengupt/
miniconf.html
20 – 21
Aston University, Birmingham, UK.
www.ima.org.uk/conferences/conferences_calendar/
maths_of_operational_research.html
23 – 28
Rostov-on-Don, Russia.
otha.sfedu.ru/conf2017
4 – 5
Ostrava, Czech Republic.
demsme.cms.opf.slu.cz/
10 – 12
Yildiz Technical University, Istanbul, Turkey.
www.icome2017.com/
11 – 15
Palm Wings Ephesus Resort Hotel, Kus Adasi, Turkey.
www.icrapam.org
20 – 22
Istanbul, Turkey.
cmes.sciencesconf.org
28 – June 3
Paseky nad Jizerou, Czech Republic.
kma.karlin.mff.cuni.cz/ss/jun17/index.php
5 – July 14
The University of Michigan School of Public Health,
Ann Arbor, MI.
www.bigdatasummerinstitute.com
January 2017 Notices of the AMS 71

11 – 18
Department of Mathematics, Sichuan University,
Chengdu, Republic of China.
isfe.up.krakow.pl/55
25 – 30
University of Muenster, Muenster, Germany.
wwwmath.uni-muenster.de/sfb878/activities/
AFF_announce.html
3 – 7
Centre de Recerca Matemàtica, Campus de Bellaterra,
Edifici C 8193 Bellaterra (Barcelona), Spain.
www.crm.cat/en/Activities/Curs_2016-2017/
Pages/Finite-Dimensional-Integrable-Systems-in-
Geometry-and-Mathematical-Physics.aspx
3 – 7
Stockholm, Sweden.
https://www.math-stockholm.se/konferenseroch-akti/young-topologists-meeting-2017-1.670396
10 – 14
Institute of Mathematics and Informatics of the Bulgarian
Academy of Sciences, Sofia, Bulgaria.
mds2017.math.bas.bg
AMERICAN MATHEMATICAL SOCIETY
10 – 19
University of Barcelona, Spain.
www.ub.edu/focm2017
24 – 28
Iowa State University, Ames, Iowa.
ilas2017.math.iastate.edu
Spend smart.
Search better.
Stay informed.
bookstore.ams.org
facebook.com/amermathsoc
@amermathsoc
plus.google.com/+AmsOrg
31 – August 4
Universität Regensburg, Germany.
www.uni-regensburg.de/mathematics/natrop2017
12 – 14
2
Washington University in St. Louis, Saint Louis, MO.
www.math.wustl.edu/~kuffner/WHOA-PSI-2.html
28 – September 1
Columbia University, New York, NY.
goo.gl/aKmSx6
2 – 6
Budapest, Hungary.
www.renyi.hu/conferences/ll70
72 Notices of the AMS Volume 64, Number 1

COMMUNICATION
2017 Annual Meeting of the
American Association for the
Advancement of Science
The 2017 annual meeting of the American Association for
the Advancement of Science will take place in Boston February
16–20. The theme of the meeting is “Serving Society
Through Science Policy.” There are several sessions which
should be of special interest to mathematicians.
Alice Silverberg of the University of California, Irvine,
has organized a symposium on “Cybersecurity: Mathematics
and Policy‚” scheduled for Sunday, February 19, 2017:
1:00 pm–2:30 pm. This panel brings together experts on
cybersecurity, cybersecurity policy, and relevant fields
of mathematics to discuss what is new and debate the
latest controversies. Presentations will be followed by a
moderated, full-group discussion. Speakers and topics
are Ronald Rivest, Massachusetts Institute of Technology,
Cryptography and Cybersecurity; Nadia Heninger, University
of Pennsylvania, The Mathematics of Cryptographic
Security; and Susan Landau, Worcester Polytechnic Institute
Cybersecurity and Privacy: A Surprising Alignment.
Professor Silverberg will moderate.
Nessy Tania, Smith College, and Richard Judson,
US Environmental Protection Agency have organized a
symposium on “Supporting Environmental Decision-Making:
Modeling Complex and Noisy Biology‚” for Saturday,
February 18, 2017: 10:00 am–11:30 am. This session discusses
the promise of mathematical modeling with three
case studies. Through examples, speakers will address
the following key challenges: models must be able to integrate
data from simple levels of biological organization
and predict effects on whole animals; methods must be
scalable to be able to make predictions on tens to hundreds
of thousands of chemicals; and methods must be
robust in the face of noise in both the simple data they are
built on and the complex phenotypes they are validated
against. Speakers and topics are Nicole Kleinstreuer,
National Institutes of Health Developing, Validating, and
Applying Pathway-Based Models for Endocrine Disruption;
Kamel Mansouri, Oak Ridge Institute for Science and
Education Fellow at US Environmental Protection Agency
Consensus Models to Predict Endocrine Disruption for All
Human-Exposure Chemicals; and Matthew Betti, University
of Western Ontario Modeling Honey Bee-Plant Symbiosis
in the Presence of Environmental Toxins New features of
the 2017 meeting are fifteen minute “flash talks.” Keith
Devlin, Stanford University, will presenting one of these
on Saturday, February 18, 2017: 1:30 pm–1:45 pm; the title
is “Symbols of Success: New Representations for Teaching
and Doing Mathematics.” In the abstract, Professor Devlin
notes that while symbolic representations are powerful
in doing mathematics, it has been known since the early
1990s that much of the difficulty people have learning
mathematics is because of the symbolic interface. The
modern tablet computer (“paper on steroids”) offers
the possibilty of developing alternative representations.
Applications to K–12 mathematics teaching have already
been developed and promise to have a significant impact
on mathematics learning. We can expect novel representations
to play a role in doing (some) mathematics as well.
Andy Magid, Secretary,
Section A (Mathematics) AAAS
january 2017 Notices of the AMS 73

AMERICAN MATHEMATICAL SOCIETY
Epsilon Fund
for Young Scholars
Graduate Student Chapters
Photo by Steve Schneider/JMM Photo courtesy of Governor’s Institutes of Vermont
Thank you FOR SUPPORTING MATHEMATICS!
JMM Child Care Grants
MathSciNet®
for Developing Countries
Photo courtesy of University of the South Pacific
Photo courtesy of UMKC Graduate Student Chapter
To learn more about giving to the AMS
and our beneficiaries, visit www.ams.org/support
AMS Development Office
401-455-4111
development@ams.org

MEETINGS & CONFERENCES
General Information Regarding
Meetings & Conferences of the AMS
Speakers and Organizers: The Council has decreed that
no paper, whether invited or contributed, may be listed
in the program of a meeting of the Society unless an abstract
of the paper has been received in Providence prior
to the deadline.
Special Sessions: The number of Special Sessions at an Annual
Meeting is limited. Special Sessions at annual meetings
are held under the supervision of the Program Committee
for National Meetings and, for sectional meetings, under the
supervision of each Section Program Committee. They are
administered by the associate secretary in charge of that
meeting with staff assistance from the Meetings and
Conferences Department in Providence. (See the list of
associate secretaries on page 76 of this issue.)
Each person selected to give an Invited Address is also
invited to generate a Special Session, either by personally
organizing one or by having it organized by others.
Proposals to organize a Special Session are sometimes
solicited either by a program committee or by the associate
secretary. Other proposals should be submitted to the
associate secretary in charge of that meeting (who is an ex
officio member of the program committee) at the address
listed on page 76 of this issue. These proposals must be in
the hands of the associate secretary at least seven months
(for sectional meetings) or nine months (for national meetings)
prior to the meeting at which the Special Session is
to be held in order that the committee may consider all
the proposals for Special Sessions simultaneously. Special
Sessions must be announced in the Notices in a timely
fashion so that any Society member who so wishes may
submit an abstract for consideration for presentation in
the Special Session.
Talks in Special Sessions are usually limited to twenty
minutes; however, organizers who wish to allocate more
time to individual speakers may do so within certain
limits. A great many of the papers presented in Special
Sessions at meetings of the Society are invited papers,
but any member of the Society who wishes to do so may
submit an abstract for consideration for presentation in a
Special Session. Contributors should know that there is a
limit to the size of a single Special Session, so sometimes
all places are filled by invitation. An author may speak by
invitation in more than one Special Session at the same
meeting. Papers submitted for consideration for inclusion
in Special Sessions but not accepted will receive consideration
for a contributed paper session, unless specific
instructions to the contrary are given.
The Society reserves the right of first refusal for the publication
of proceedings of any Special Session. If published
by the AMS, these proceedings appear in the book series
Contemporary Mathematics. For more detailed information
on organizing a Special Session, see www.ams.org/
meetings/meet-specialsessionmanual.html.
Contributed Papers: The Society also accepts abstracts
for ten-minute contributed papers. These abstracts will be
grouped by related Mathematical Reviews subject classifications
into sessions to the extent possible. The title and
author of each paper accepted and the time of presentation
will be listed in the program of the meeting. Although
an individual may present only one ten-minute contributed
paper at a meeting, any combination of joint authorship
may be accepted, provided no individual speaks more
than once.
Other Sessions: In accordance with policy established
by the AMS Committee on Meetings and Conferences,
mathematicians interested in organizing a
session (for either an annual or a sectional meeting)
on employment opportunities inside or outside academia
for young mathematicians should contact the
associate secretary for the meeting with a proposal by
the stated deadline. Also, potential organizers for poster
sessions (for an annual meeting) on a topic of choice
should contact the associate secretary before the deadline.
Abstracts: Abstracts for all papers must be received by the
meeting coordinator in Providence by the stated deadline.
Unfortunately, late papers cannot be accommodated.
Submission Procedures: Visit the Meetings and Conferences
homepage on the Web at www.ams.org/
meetings and select “Submit Abstracts.”
Site Selection for Sectional Meetings
Sectional meeting sites are recommended by the associate
secretary for the section and approved by the Secretariat.
Recommendations are usually made eighteen to twentyfour
months in advance. Host departments supply local
information, ten to fifteen rooms with overhead projectors
and a laptop projector for contributed paper sessions and
Special Sessions, an auditorium with twin overhead projectors
and a laptop projector for Invited Addresses, space
for registration activities and an AMS book exhibit, and
registration clerks. The Society partially reimburses for
the rental of facilities and equipment needed to run these
meetings successfully. For more information, contact the
associate secretary for the section.
January 2017 Notices of the AMS 75

MEETINGS & CONFERENCES OF THE AMS
JANUARY TABLE OF CONTENTS
The Meetings and Conferences section of
the Notices gives information on all AMS
meetings and conferences approved by
press time for this issue. Please refer to
the page numbers cited on this page for
more detailed information on each event.
Invited Speakers and Special Sessions are
listed as soon as they are approved by the
cognizant program committee; the codes
listed are needed for electronic abstract
submission. For some meetings the list
may be incomplete. Information in this
issue may be dated.
The most up-to-date meeting and conference
information can be found online at:
www.ams.org/meetings/.
Important Information About AMS
Meetings: Potential organizers,
speakers, and hosts should refer to
page 75 in the January 2017 issue of the
Notices for general information regarding
participation in AMS meetings and
conferences.
Abstracts: Speakers should submit abstracts
on the easy-to-use interactive
Web form. No knowledge of L A TEX is
necessary to submit an electronic form,
although those who use L A TEX may submit
abstracts with such coding, and all math
displays and similarily coded material
(such as accent marks in text) must
be typeset in L A TEX. Visit www.ams.org/
cgi-bin/abstracts/abstract.pl/. Questions
about abstracts may be sent to absinfo@ams.org.
Close attention should be
paid to specified deadlines in this issue.
Unfortunately, late abstracts cannot be
accommodated.
MEETINGS IN THIS ISSUE
–––––––– 2017 ––––––––
January 4–7 JMM 2017— Atlanta p. 77
March 10–12 Charleston, South Carolina p. 80
April 1–2 Bloomington, Indiana p. 85
April 22–23 Pullman, Washington p. 86
May 6–7 New York, New York p. 87
July 24–28 Montréal, Quebec, Canada p. 88
September 9–10 Denton, Texas p. 90
September 16–17 Buffalo, New York p. 91
September 23–24 Orlando, Florida p. 91
November 4–5 Riverside, California p. 92
–––––––– 2018 ––––––––
January 10–13 San Diego, California p. 92
March 24–25 Columbus, Ohio p. 92
April 14–15 Nashville, Tennesse p. 93
April 14–15 Portland, Oregon p. 93
April 21–22 Boston, Massachusetts p. 93
June 11–14 Shanghai, People's Republic
of China p. 93
–––––––– 2018 , cont'd. ––––––––
September 29–30 Newark, Delaware p. 93
October 27–28 San Francisco, California p. 94
–––––––– 2019 ––––––––
January 16–19 Baltimore, Maryland p. 94
March 29–31 Honolulu, Hawaii p . 9 4
–––––––– 2020 ––––––––
January 15–18 Denver, Colorado p. 94
–––––––– 2021 ––––––––
January 6–9 Washington, DC p. 94
See www.ams.org/meetings/ for the most up-to-date information on these conferences.
Central Section: Georgia Benkart, University of Wisconsin-
Madison, Department of Mathematics, 480 Lincoln Drive,
Madison, WI 53706-1388; e-mail: benkart@math.wisc.edu;
telephone: 608-263-4283.
ASSOCIATE SECRETARIES OF THE AMS
Southeastern Section: Brian D. Boe, Department of Mathematics,
University of Georgia, 220 D W Brooks Drive, Athens, GA
30602-7403, e-mail: brian@math.uga.edu; telephone: 706-
542-2547.
Eastern Section: Steven H. Weintraub, Department of Mathematics,
Lehigh University, Bethlehem, PA 18015-3174; e-mail:
steve.weintraub@lehigh.edu; telephone: 610-758-3717.
Western Section: Michel L. Lapidus, Department of Mathematics,
University of California, Surge Bldg., Riverside, CA 92521-
0135; e-mail: lapidus@math.ucr.edu; telephone: 951-827-5910.
76 NOTICES OF THE AMS VOLUME 64, NUMBER 1

MEETINGS & CONFERENCES
Meetings & Conferences of the AMS
Meetings Conferences of the AMS
IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear
in the print version of the Notices. However, comprehensive and continually updated meeting and program information
with links to the abstract for each talk can be found on the AMS website. See www.ams.org/meetings/.
Final programs for Sectional Meetings will be archived on the AMS website accessible from the stated URL .
Atlanta, Georgia
Hyatt Regency Atlanta and
Marriott Atlanta Marquis
January 4–7, 2017
Wednesday – Saturday
Meeting #1125
Joint Mathematics Meetings, including the 123rd Annual
Meeting of the AMS, 100th Annual Meeting of the Mathematical
Association of America, annual meetings of the
Association for Women in Mathematics (AWM) and the
National Association of Mathematicians (NAM), and the
winter meeting of the Association of Symbolic Logic, with
sessions contributed by the Society for Industrial and Applied
Mathematics (SIAM).
Associate secretary: Brian D. Boe
Announcement issue of Notices: October 2016
Program first available on AMS website: To be announced
Issue of Abstracts: Volume 38, Issue 1
Deadlines
For organizers: Expired
For abstracts: Expired
The scientific information listed below may be dated.
For the latest information, see www.ams.org/amsmtgs/
national.html.
Joint Invited Addresses
Ingrid Daubechies, Duke University, Mathematics for
art investigation (MAA-AMS-SIAM Gerald and Judith Porter
Public Lecture).
Lisa Jeffrey, University of Toronto, Real loci in symplectic
manifolds (AWM-AMS Noether Lecture).
Donald Richards, Penn State University, Distance Correlation:
A New Tool for Detecting Association and Measuring
Correlation Between Data Sets (AMS-MAA Invited Address).
Alice Silverberg, University of California, Irvine,
Through the Cryptographer’s Looking-Glass, and what
Alice found there (AMS-MAA Invited Address).
AMS Invited Addresses
Tobias Holck Colding, Massachusetts Institute of Technology,
Arrival time.
Carlos E. Kenig, University of Chicago, Overview: The
focusing energy critical wave equation (AMS Colloquium
Lectures: Lecture I).
Carlos E. Kenig, University of Chicago, The focusing
energy critical wave equation: the non-radial case (AMS
Colloquium Lectures: Lecture III).
Carlos E. Kenig, University of Chicago, The focusing
energy critical wave equation: the radial case in 3 space
dimensions (AMS Colloquium Lectures: Lecture II).
John Preskill, California Institute of Technology, Quantum
computing and the entanglement frontier (AMS Josiah
Willard Gibbs Lecture).
Barry Simon, Caltech, Spectral Theory Sum Rules, Meromorphic
Herglotz Functions and Large Deviations.
Gigliola Staffilani, Massachusetts Institute of Technology,
The many faces of dispersive and wave equations.
Richard Taylor, Institute for Advanced Study, Galois
groups and locally symmetric spaces.
Anna Wienhard, Ruprecht-Karls-Universität Heidelberg,
A tale of rigidity and flexibility—discrete subgroups of
higher rank Lie groups.
AMS Special Sessions
If you are volunteering to speak in a Special Session,
you should send your abstract as early as possible
via the abstract submission form found at
jointmathematicsmeetings.org/meetings/
abstracts/abstract.pl?type=jmm.
Some sessions are cosponsored with other organizations.
These are noted within the parenthesis at the end
of each listing, where applicable.
Advanced Mathematical Programming and Applications,
Ram N. Mohapatra, University of Central Florida,
January 2017 Notices of the AMS 77

MEETINGS & CONFERENCES
Ram U. Verma, University of North Texas, and Gayatri
Pany, Indian Institute of Technology.
Advances in Mathematics of Ecology, Epidemiology and
Immunology of Infectious Diseases, Abba Gumel, Arizona
State University.
Advances in Numerical Analysis for Partial Differential
Equations, Thomas Lewis, University of North Carolina
at Greensboro, and Amanda Diegel, Louisiana State University.
Advances in Operator Algebras, Michael Hartglass,
University of California, Riverside, David Penneys, University
of California, Los Angeles, and Elizabeth Gillaspy,
University of Colorado, Boulder.
Algebraic Statistics (a Mathematics Research Communities
Session), Mateja Raic, University of Illinois at Chicago,
Nathaniel Bushnek, University of Alaska, Anchorage, and
Daniel Irving Bernstein, North Carolina State University.
An Amicable Combination of Algebra and Number
Theory (Dedicated to Dr. Helen G. Grundman), Eva Goedhart,
Lebanon Valley College, Pamela E. Harris, Williams
College, Daniel P. Wisniewski, DeSales University, and
Alejandra Alvarado, Eastern Illinois University.
Analysis of Fractional, Stochastic, and Hybrid Dynamic
Systems and their Applications, Aghalaya S. Vatsala,
University of Louisiana at Lafayette, Gangaram S. Ladde,
University of South Florida, and John R. Graef, University
of Tennessee at Chattanooga.
Analytic Number Theory and Arithmetic, Robert Lemke
Oliver, Tufts University, Paul Pollack, University of Georgia,
and Frank Thorne, University of South Carolina.
Analytical and Computational Studies in Mathematical
Biology, Yanyu Xiao, University of Cincinnati, and Xiang-
Sheng Wang, University of Louisiana at Lafayette.
ApREUF: Applied Research Experience for Undergraduate
Faculty, Shenglan Yuan, LaGuardia Community College,
CUNY, Jason Callahan, St. Edwards University, Eva
Strawbridge, James Madison University, and Ami Radunskaya,
Pomona College.
Applications of Partially Ordered Sets in Algebraic,
Topological, and Enumerative Combinatorics, Rafael S.
González D’León, University of Kentucky, and Joshua
Hallam, Wake Forest University.
Arithmetic Properties of Sequences from Number Theory
and Combinatorics, Eric Rowland, Hofstra University, and
Armin Straub, University of South Alabama.
Automorphic Forms and Arithmetic, Frank Calegari,
University of Chicago, Ana Caraiani, Princeton University,
and Richard Taylor, Institute for Advanced Study.
Bases in Function Spaces: Sampling, Interpolation, Expansions
and Approximations, Shahaf Nitzan and Christopher
Heil, Georgia Institute of Technology, and Alexander
V. Powell, Vanderbilt University.
Character Varieties (a Mathematics Research Communities
Session), Nathan Druivenga, University of Kentucky,
Brett Frankel, Northwestern University, and Ian Le, Perimeter
Institute for Theoretical Physics.
Coding Theory for Modern Applications, Christine A.
Kelley, University of Nebraska-Lincoln, Iwan M. Duursma,
University of Illinois Urbana-Champaign, and Gretchen L.
Matthews, Clemson University.
Combinatorial and Cohomological Invariants of Flag
Manifolds and Related Varieties, Martha Precup, Northwestern
University, and Rebecca Goldin, George Mason
University.
Commutative Algebra: Research for Undergraduate
and Early Graduate Students, Nicholas Baeth, University
of Central Missouri, and Courtney Gibbons, Hamilton
College.
Complex Analysis and Special Functions, Brock Williams,
Texas Tech University, Kendall Richards, Southwestern
University, and Alex Solynin, Texas Tech University.
Continued Fractions, James McLaughlin, West Chester
University, Geremías Polanco, Hampshire College, and
Nancy J. Wyshinski, Trinity College.
Control and Long Time Behavior of Evolutionary PDEs,
Louis Tebou, Florida International University, and Luz de
Teresa, Instituto de Matemáticas, UNAM.
Discrete Geometry and Convexity (Dedicated to András
Bezdek on the occasion of his 60th birthday), Krystyna
Kuperberg, Auburn University, Gergely Ambrus, Renyi
Institute of Mathematics, Braxton Carrigan, Southern
Connecticut State University, and Ferenc Fodor, University
of Szeged.
Discrete Structures in Number Theory, Anna Haensch,
Duquesne University, and Adriana Salerno, Bates College.
Dynamical Systems, Jim Wiseman, Agnes Scott College,
and Aimee Johnson, Swarthmore College.
Dynamics of Fluids and Nonlinear Waves, Zhiwu Lin,
Jiayin Jin, and Chongchun Zeng, Georgia Institute of
Technology.
Ergodic Theory and Dynamical Systems, Mrinal Kanti
Roychowdhury, University of Texas Rio Grande Valley,
and Tamara Kucherenko, City College of New York.
Fusion Categories and Quantum Symmetries, Julia
Plavnik, Texas A&M University, Paul Bruillard, Pacific
Northwest National Laboratory, and Eric Rowell, Texas
A&M University.
Gaussian Graphical Models and Combinatorial Algebraic
Geometry, Rainer Sinn, Georgia Institute of Technology,
Seth Sullivant, North Carolina State University, and
Josephine Yu, Georgia Institute of Technology.
Graphs and Matrices, Sudipta Mallik, Northern Arizona
University, Keivan Hassani Monfared, University of Calgary,
and Bryan Shader, University of Wyoming.
Group Actions and Geometric Structures, Anna Wienhard,
Universität Heidelberg, and Jeffrey Danciger, University
of Texas at Austin.
Group Representations and Cohomology, Hung Nguyen,
The University of Akron, Nham Ngo, The University of
Arizona, Andrei Pavelescu, University of South Alabama,
and Paul Sobaje, University of Georgia.
78 Notices of the AMS Volume 64, Number 1

MEETINGS & CONFERENCES
Harmonic Analysis (In Honor of Gestur Olafsson’s 65th
Birthday), Jens Christensen, Colgate University, and Susanna
Dann, Technische Universität Wien-Vienna, Austria.
History of Mathematics, Adrian Rice, Randolph-Macon
College, Sloan Despeaux, Western Carolina University, and
Daniel Otero, Xavier University (AMS-MAA-ICHM).
Hopf Algebras and their Actions, Henry Tucker, University
of California, San Diego, Susan Montgomery, University
of Southern California - Los Angeles, and Siu-Hung
Ng, Louisiana State University.
Inverse Problems and Applications, Vu Kim Tuan and
Amin Boumenir, University of West Georgia.
Inverse Problems and Multivariate Signal Analysis,
M. Zuhair Nashed, University of Central Florida, Willi
Freeden, University of Kaiserslautern, and Otmar Scherzer,
University of Vienna.
Lie Group Representations, Discretization, and Gelfand
Pairs (a Mathematics Research Communities Session), Matthew
Dawson, CIMAT, Holley Friedlander, Dickenson
College, John Hutchens, Winston-Salem State University,
and Wayne Johnson, Truman State University.
Mapping Class Groups and their Subgroups, James W.
Anderson, University of Southampton, UK, and Aaron
Wootton, University of Portland.
Mathematics and Music, Mariana Montiel, Georgia State
University, and Robert Peck, Louisiana State University.
Mathematics in Physiology and Medicine (a Mathematics
Research Communities Session), Kamila Larripa, Humboldt
State University, Charles Puelz, Rice University, Laura
Strube, University of Utah, and Longhua Zhao, Case Western
Reserve University.
Mathematics of Cryptography, Nathan Kaplan and Alice
Silverberg, University of California, Irvine (AMS-MAA).
Mathematics of Signal Processing and Information,
Rayan Saab, University of California, San Diego, and Mark
Iwen, Michigan State University.
Measure and Measurable Dynamics (In Memory of Dorothy
Maharam, 1917-2014), Cesar Silva, Williams College.
Minimal Integral Models of Algebraic Curves, Tony
Shaska, Oakland University.
NSFD Discretizations: Recent Advances, Applications,
and Unresolved Issues, Talitha M. Washington, Howard
University, and Ronald E. Mickens, Clark Atlanta University.
New Developments in Noncommutative Algebra & Representation
Theory, Ellen Kirkman, Wake Forest University,
and Chelsea Walton, Temple University.
Nonlinear Systems and Applications, Wenrui Hao, Ohio
State University.
Open & Accessible Problems for Undergraduate Research,
Allison Henrich, Seattle University, Michael Dorff,
Brigham Young University, and Nicholas Scoville, Ursinus
College.
Operator Theory, Function Theory, and Models, William
Ross, University of Richmond, and Alberto Condori,
Florida Golf Coast University.
Orthogonal Polynomials, Doron Lubinsky and Jeff
Geronimo, Georgia Institute of Technology.
PDE Analysis on Fluid Flows, Xiang Xu, Old Dominion
University, and Geng Chen and Ronghua Pan, Georgia
Institute of Technology.
PDEs for Fluid flow: Analysis and Computation, Thinh
Kieu, University of North Georgia, Emine Celik, University
of Nevada, Reno, and Hashim Saber, University of North
Georgia.
Partition Theory and Related Topics, Amita Malik, University
of Illinois at Urbana-Champaign, Dennis Eichhorn,
University of California, Irvine, and Tim Huber, University
of Texas-Rio Grande Valley.
Problems in Partial Differential Equations, Alex Himonas,
University of Notre Dame, and Dionyssios Mantzavinos,
State University of New York at Buffalo.
Public School Districts and Higher Education Mathematics
Partnerships, Virgil U. Pierce and Aaron Wilson, University
of Texas Rio Grande Valley.
Pure and Applied Talks by Women Math Warriors Presented
by EDGE (Enhancing Diversity in Graduate Education),
Candice Price, University of San Diego, and Amy
Buchman, Tulane University.
Quantum Groups, Shuzhou Wang and Angshuman
Bhattacharya, University of Georgia.
Quaternions, Johannes Familton, Borough of Manhattan
Community College, Terrence Blackman, Medgar
Evers College, and Chris McCarthy, Borough of Manhattan
Community College.
RE(UF)search on Graphs and Matrices, Cheryl Grood,
Swarthmore College, Daniela Ferrero, Texas State University,
and Mary Flagg, University of St. Thomas.
Random Matrices, Random Percolation and Random
Sequence Alignments, Ruoting Gong, Illinois Institute of
Technology, and Michael Damron, Georgia Institute of
Technology.
Real Discrete Dynamical Systems with Applications,
M. R. S. Kulenovic, University of Rhode Island, and Abdul-
Aziz Yakubu, Howard University.
Recent Advances in Mathematical Biology, Zhisheng
Shuai, University of Central Florida, Guihong Fan, Columbus
State University, Andrew Nevai, University of Central
Florida, and Eric Numfor, Augusta University.
Recent Progress on Nonlinear Dispersive and Wave
Equations, Dana Mendelson, Carlos Kenig, and Hao Jia,
University of Chicago, Andrew Lawrie, University of
California, Berkeley, Gigliola Staffilani, Massachusetts Institute
of Technology, and Magdalena Czubak, University
of Colorado Boulder.
Representations and Related Geometry in Lie Theory,
Laura Rider, Massachusetts Institute of Technology, and
Amber Russell, Butler University.
Research in Mathematics by Undergraduates and Students
in Post-Baccalaureate Programs, Darren A. Narayan,
Rochester Institute of Technology, Tamas Forgacs, California
State University, Fresno, and Ugur Abdulla, Florida
Institute of Technology (AMS-MAA-SIAM).
Sheaves in Topological Data Analysis, Mikael Vejdemo-
Johansson, CUNY College of Staten Island, Elizabeth
January 2017 Notices of the AMS 79

MEETINGS & CONFERENCES
Munch, University at Albany, SUNY, and Martina Scolamiero,
École polytechnique fédérale de Lausanne.
Spectral Calculus and Quasilinear Partial Differential
Equations, Shijun Zheng, Georgia Southern University,
Marius Beceanu, State University of New York - Albany,
and Tuoc Van Phan, University of Tennessee, Knoxville.
Spin Glasses and Disordered Media, Antonio Auffinger,
Northwestern University, Aukosh Jagannath, New York
University, and Dmitry Panchenko, University of Toronto.
Statistical Methods in Computational Topology and
Applications, Yu-Min Chung and Sarah Day, College of
William & Mary.
Stochastic Matrices and Their Applications, Selcuk
Koyuncu, University of North Georgia, and Lei Cao, Georgian
Court University.
Stochastic Processes and Modelling, Erkan Nane, Auburn
University, and Jebessa B. Mijena, Georgia College and
State University.
Symmetries, Integrability, and Beyond, Maria Clara
Nucci, Università di Perugia, ITALY, and Sarah Post, University
of Hawaií at Manoa.
Symplectic Geometry, Moment Maps and Morse Theory,
Lisa Jeffrey, University of Toronto, and Tara Holm, Cornell
University (AMS-AWM).
Teaching Assistant Development Programs: Why
and How?, Solomon Friedberg, Boston College, Jessica
Deshler, West Virginia University, Jeffrey Remmel,
University of California, San Diego, and Lisa Townsley,
University of Georgia.
The Mathematics of the Atlanta University Center,
Talitha M. Washington, Howard University, Monica Jackson,
American University, and Colm Mulcahy, Spelman
College (AMS-NAM).
The Modeling First Approach to Teaching Differential
Equations, Chris McCarthy, City University of New York,
and Brian Winkel, US Military Academy, West Point.
Theory and Applications of Numerical Algebraic Geometry,
Daniel Brake, University of Notre Dame, Robert
Krone, Queen’s University, and Jose Israel Rodriguez,
University of Chicago.
Topics in Graph Theory, Songling Shan, Vanderbilt
University, and Xiaofeng Gu, University of West Georgia.
Topology, Representation Theory, and Operator Algebras
(A Tribute to Paul Baum), Efton Park and Jose Carrion,
Texas Christian University.
Women in Analysis (In Honor of Cora Sadosky), Alexander
Reznikov, Vanderbilt University, Oleksandra
Beznosova and Hyun-Kyoung Kwon, University of Alabama,
and Katharine Ott, Bates College.
Women in Topology, Jocelyn Bell, Hobart and William
Smith Colleges, Eleanor Ollhoff, University of Tennessee,
Candice Price, University of San Diego, and Arunima Ray,
Brandeis University.
Charleston, South
Carolina
College of Charleston
March 10–12, 2017
Friday – Sunday
Meeting #1126
Southeastern Section
Associate secretary: Brian D. Boe
Announcement issue of Notices: January
Program first available on AMS website: January 23, 2017
Issue of Abstracts: Volume 38, Issue 2
Deadlines
For organizers: Expired
For abstracts: January 17, 2017
The scientific information listed below may be dated.
For the latest information, see www.ams.org/amsmtgs/
sectional.html.
Invited Addresses
Pramod N. Achar, Louisiana State University, Representations
of algebraic groups via algebraic topology.
Hubert Bray, Duke University, The Geometry of Special
and General Relativity.
Alina Chertock, North Carolina State University, Numerical
methods for chemotaxis and related models.
Special Sessions
If you are volunteering to speak in a Special Session, you
should send your abstract as early as possible via the abstract
submission form found at www.ams.org/cgi-bin/
abstracts/abstract.pl.
Active Learning in Undergraduate Mathematics (Code:
SS 21A), Draga Vidakovic, Georgia State University, Harrison
Stalvey, University of Colorado, Boulder, and Darryl
Chamberlain,Jr., Aubrey Kemp, and Leslie Meadows,
Georgia State University.
Advances in Long-term Behavior of Nonlinear Dispersive
Equations (Code: SS 27A), Brian Pigott, Wofford College,
and Sarah Raynor, Wake Forest University.
Advances in Nonlinear Waves: Theory and Applications
(Code: SS 23A), Constance M. Schober, University of Central
Florida, and Andrei Ludu, Embry Riddle University.
Algebras, Lattices, Varieties (Code: SS 19A), George F.
McNulty, University of South Carolina, and Kate S. Owens,
College of Charleston.
Analysis and Control of Fluid-Structure Interactions and
Fluid-Solid Mixtures (Code: SS 6A), Justin T. Webster, College
of Charleston, and Daniel Toundykov, University of
Nebraska-Lincoln.
80 Notices of the AMS Volume 64, Number 1

MEETINGS & CONFERENCES
Analysis, Control and Stabilization of PDE’s (Code: SS
13A), George Avalos, University of Nebraska-Lincoln, and
Scott Hansen, Iowa State University.
Bicycle Track Mathematics (Code: SS 25A), Ron Perline,
Drexel University.
Coding Theory, Cryptography, and Number Theory
(Code: SS 17A), Jim Brown, Shuhong Gao, Kevin James,
Felice Manganiello, and Gretchen Matthews, Clemson
University.
Commutative Algebra (Code: SS 1A), Bethany Kubik,
University of Minnesota Duluth, Saeed Nasseh, Georgia
Southern University, and Sean Sather-Wagstaff, Clemson
University.
Computability in Algebra and Number Theory (Code:
SS 8A), Valentina Harizanov, The George Washington
University, Russell Miller, Queens College and Graduate
Center - City University of New York, and Alexandra Shlapentokh,
East Carolina University.
Data Analytics and Applications (Code: SS 2A), Scott C.
Batson, Lucas A. Overbuy, and Bryan Williams, Space
and Naval Warfare Systems Center Atlantic.
Factorization and Multiplicative Ideal Theory (Code:
SS 16A), Jim Coykendall, Clemson University, and Evan
Houston and Thomas G. Lucas, University of North Carolina,
Charlotte.
Fluid-Boundary Interactions (Code: SS 26A), M. Nick
Moore, Florida State University.
Frame Theory (Code: SS 22A), Dustin Mixon, Air Force
Institute of Technology, John Jasper, University of Cincinnati,
and James Solazzo, Coastal Carolina University.
Free-boundary Fluid Models and Related Problems
(Code: SS 7A), Marcelo Disconzi, Vanderbilt University,
and Lorena Bociu, North Carolina State University.
Geometric Analysis and General Relativity (Code: SS
20A), Hubert L. Bray, Duke University, Otis Chodosh,
Princeton University, and Greg Galloway and Pengzi Miao,
University of Miami.
Geometric Methods in Representation Theory (Code: SS
15A), Pramod N. Achar, Louisiana State University, and
Amber Russell, Butler University.
Geometry and Symmetry in Integrable Systems (Code:
SS 10A), Annalisa Calini, Alex Kasman, and Thomas Ivey,
College of Charleston.
Graph Theory (Code: SS 5A), Colton Magnant, Georgia
Southern University, and Zixia Song, University of Central
Florida.
Knot Theory and its Applications (Code: SS 3A), Elizabeth
Denne, Washington & Lee University, and Jason
Parsley, Wake Forest University.
Nonlinear Waves: Analysis and Numerics (Code: SS
18A), Anna Ghazaryan, Miami University, St é phane
Lafortune, College of Charleston, and Vahagn Manukian,
Miami University.
Numerical Methods for Coupled Problems in Computational
Fluid Dynamics (Code: SS 11A), Vincent J. Ervin and
Hyesuk Lee, Clemson University.
Oscillator Chain and Lattice Models in Optics, the
Power Grid, Biology, and Polymer Science (Code: SS 14A),
Alejandro Aceves, Southern Methodist University, and
Brenton LeMesurier, College of Charleston.
Recent Trends in Finite Element Methods (Code: SS 9A),
Michael Neilan, University of Pittsburgh, and Leo Rebholz,
Clemson University.
Representation Theory and Algebraic Mathematical
Physics (Code: SS 12A), Iana I. Anguelova, Ben Cox, and
Elizabeth Jurisich, College of Charleston.
Riemann-Hilbert Problem Approach to Asymptotic
Problems in Integrable Systems, Orthogonal Polynomials
and Other Areas (Code: SS 24A), Alexander Tovbis, University
of Central Florida, and Robert Jenkins, University
of Arizona.
Rigidity Theory and Inversive Distance Circle Packings
(Code: SS 4A), John C. Bowers, James Madison University,
and Philip L. Bowers, The Florida State University.
There will be a cocktail hour hosted by the College of
Charleston Department of Mathematics on Saturday at
6:00pm in the Atrium of the School of Sciences and Mathematics
Building.
Accommodations
Participants should make their own arrangements directly
with the hotel of their choice. Special discounted rates
were negotiated with the hotels listed below. Rates quoted
do not include a room tax of 13.5 percent and $1.00 occupancy
fee per room per night. Participants must state
that they are with the American Mathematical Society
(AMS) Meeting at the College of Charleston to receive
the discounted rate. The AMS is not responsible for rate
changes or for the quality of the accommodations. Hotels
have varying cancellation and early checkout penalties;
be sure to ask for details.
Comfort Inn (1.1 mi from the School of Sciences and
Mathematics Building), 144 Bee Street, Charleston, SC
29401; online: https://www.choicehotels.com/southcarolina/charleston/comfort-inn-hotels/sc099
or
by phone: 843-577-2224. Rates are US$129 for standard
rooms. This rate includes parking, wifi and hot breakfast
buffet. Please cite the American Mathematical Society
code: AMS when making your reservation. Amenities at
the Comfort Inn include a business center and a fitness
room. Deadline for reservations is February 9, 2017.
Holiday Inn Express Charleston Downtown - Ashley
River (1.3 mi from the School of Sciences and Mathematics
Building), 250 Spring Street, Charleston, SC 29403; online:
www.hiexpress.com/charlestondwtn or by phone:
843-722-4000. Rates are US$139 for standard rooms
Thursday night and US$189 for standard rooms on Friday
and Saturday nights. All rooms include complimentary hot
breakfast buffet and high speed internet service. Please
cite the American Mathematical Society code: AMS
when making your reservation. Guests are welcome to use
Holiday Express' on-site fitness center and outdoor pool
as well as their full service business center. There is no
January 2017 Notices of the AMS 81

MEETINGS & CONFERENCES
charge for parking at the Holiday Inn Express. Deadline
for reservations is February 9, 2017.
La Quinta Inn Charleston Riverview (1.8 mi from the
School of Sciences and Mathematics Building) 11 Ashley
Pointe Drive, Charleston, SC 29407, online: www.lq.com/
en/findandbook/hotel-details.charleston-riverview.html
or by phone: 843-556-5200. Rates are US$145
for a standard room. Please cite the American Mathematical
Society code: AMS when making your reservation. All
rooms and suites offer complimentary wireless internet,
complimentary breakfast and complimentary parking. La
Quinta Inn's amenities include a business center, a fitness
center, and an outdoor pool. Deadline for reservations is
February 16, 2017.
Quality Inn & Suites Patriots Point (4.3 mi from the School
of Sciences and Mathematics Building) 196 Patriots Point
Rd, Mount Pleasant, SC, 29464, online: choicehotels.
com/south-carolina/mount-pleasant/quality-innhotels/sc064
or by phone: 843-856-8817. Rates are
US$129.99 for a standard room. Please cite the American
Mathematical Society code: AMS when making your reservation.
Rooms include complimentary wireless internet,
complimentary breakfast and complimentary parking.
Amenities at the Comfort Suites Arena include a business
center, a fitness center, and an outdoor pool. Deadline for
reservations is February 9, 2016.
Town and Country Inn and Suites (5.5 mi from the School
of Sciences and Mathematics Building) 2008 Savannah
Hwy. Charleston, SC, 29401, online: thetownandcountryinn.com/index.cfm
or by phone: 843-571-1000. Rates
are US$109 on Thursday night and US $149 on Friday and
Saturday nights. Please cite the American Mathematical
Society code: AMS when making your reservation. All
rooms offer complimentary wireless internet, and complimentary
parking. Town and Country Inn and Suites'
amenities include a business center, a fitness center, and
an outdoor pool. Deadline for reservations is February
9, 2017.
Hampton Inn Charleston Mount Pleasant Patriot Point
(4.6 mi from the School of Sciences and Mathematics
Building) 255 Sessions Way, Mount Pleasant, South
Carolina, 29464, online: hamptoninn3.hilton.com/en/
hotels/south-carolina/hampton-inn-charlestonmt-pleasant-patriots-point-CHSMTHX/index.html
or by phone: 843-881-3300. Rates are US$149 for a standard
room. Please cite the American Mathematical Society
code: AMS when making your reservation. All rooms
offer complimentary wireless internet, complimentary
breakfast, and complimentary parking. Hampton Inn's
amenities include a business center, a fitness center, and
an outdoor pool. Deadline for reservations is February
7, 2017.
Holiday Inn Express Mount Pleasant (5.1 mi from
the School of Sciences and Mathematics Building) 350
Johnnie Dodds Blvd, Mount Pleasant, SC 29464, online:
https://www.ihg.com/holidayinnexpress/hotels/
us/en/mount-pleasant/chsgr/hoteldetail# or by
phone: 843-375-2600. Rates are US$119 on Thursday night
and US$159 on Friday and Saturday nights. Please cite the
American Mathematical Society code: AMS when making
your reservation. All rooms offer complimentary wireless
internet, complimentary breakfast, and complimentary
parking. Holiday Inn Express' amenities include a business
center, a fitness center, and an outdoor pool. Deadline for
reservations is February 9, 2017.
Food Services and Dining
On Campus: There will be no on campus dining during
the meeting as College of Charleston will be on Spring
Break and all on campus dining facilities will be closed.
There are numerous walkable off-campus dining options.
Off-Campus: Charleston is a culinary hotspot and you'll
find a broad spectrum of restaurants and eateries within a
five block radius of the meeting. The following restaurants
are just a few of the many restaurants open for both lunch
and dinner that are walkable from the meeting:
Swamp Fox Restaurant, 387 King Street
(francismarionhotel.com/dining) Featuring Lowcountry
specialties reminiscent of the old south. Award-winning
shrimp & grits and Certified SC farm fresh ingredients
artfully prepared by Chef James.
Virginia's on King, 412 King Street
(holycityhospitality.com/virginias-on-king) A
collection of family recipes and southern tradition, Virginia's
on King specializes in upscale Low country cuisine.
Caviar and Bananas, 51 George Street
(caviarandbananas.com) Gourmet market and cafe.
Verde, 347 King Street (eatatverde.com) Fresh, bright
and satisfying health food. Salads, wraps and signature
creations.
Vincent Chicco's, 39-G John Street
(holycityhospitality.com/vincent-chiccos) Serves
Italian-American cuisine, celebrating classic flavors and
domestic ingredients in a sophisticated atmosphere.
Mello Mushroom, 309 King Street (mellowmushroom.
com) Casual. Pizza, salads, burgers and sandwiches.
Basil, 460 King Street (eatatbasil.com) Refined Thai
cuisine and an invigorating dining experience. Indoor and
outdoor dining.
For an extensive listing of casual and upscale dining
options near the College of Charleston, please
visit charlestoncvb.com/plan-your-trip/diningnightlife~124/.
82 Notices of the AMS Volume 64, Number 1

MEETINGS & CONFERENCES
Registration and Meeting Information
Advance Registration
Advance registration for this meeting will open on
January 25, 2017. Advance registration fees will be US$59
for AMS members, US$85 for nonmembers, and US$10
for students, unemployed mathematicians, and emeritus
members. Participants may cancel registrations made
in advance by e-mailing mmsb@ams.org. The deadline to
cancel is the first day of the meeting.
On-site Information and Registration
The Registration Desk and the AMS Book Exhibit will be
located in the School of Sciences and Mathematics Building
(202 Calhoun Street).
The Registration Desk will be open on Friday,
March 10, 1:30 pm–5:00 pm and Saturday, March 11,
7:30 am–4:30 pm. The same fees apply for on-site registration,
as for advance registration. Fees are payable on-site
via cash, check, or credit card. Invited Addresses will also
be held in the School of Sciences and Mathematics Building
(202 Calhoun Street). Special Sessions and Sessions for
Contributed Papers will be held in the School of Sciences
and Mathematics Building (202 Calhoun Street), Robert
Scott Small Building (175 Calhoun Street), and Maybank
Hall (169 Calhoun Street).
Other Activities
Book Sales: Stop by the on-site AMS bookstore to review
the newest publications and take advantage of exhibit
discounts and free shipping on all on-site orders! AMS
members receive 40 percent off list price. Nonmembers
receive a 25 percent discount. Not a member? Ask a
representative about the benefits of AMS membership.
Complimentary coffee will be served courtesy of AMS
Membership Services.
AMS Editorial Activity: An acquisitions editor from the
AMS book program will be present to speak with prospective
authors. If you have a book project that you would like
to discuss with the AMS, please stop by the book exhibit.
Special Needs
It is the goal of the AMS to ensure that its conferences
are accessible to all, regardless of disability. The AMS will
strive, unless it is not practicable, to choose venues that
are fully accessible to the physically handicapped.
If special needs accommodations are necessary in order
for you to participate in an AMS Sectional Meeting, please
communicate your needs in advance to the AMS Meetings
Department by:
- Registering early for the meeting
- Checking the appropriate box on the registration
form, and
- Sending an e-mail request to the AMS Meetings Department
at mmsb@ams.org or meet@ams.org.
Complimentary Coffee will be served courtesy of AMS
membership services.
AMS Policy on a Welcoming Environment
The AMS strives to ensure that participants in its activities
enjoy a welcoming environment. In all its activities, the
AMS seeks to foster an atmosphere that encourages the
free expression and exchange of ideas. The AMS supports
equality of opportunity and treatment for all participants,
regardless of gender, gender identity, or expression, race,
color, national or ethnic origin, religion or religious belief,
age, marital status, sexual orientation, disabilities, or
veteran status.
Local Information and Maps
This meeting will take place on the College of Charleston
campus. A campus map can be viewed at cofc.edu/
visit/campusmaps.php. Information about the College
of Charleston Department of Mathematics can be found
on their website at math.cofc.edu/ Please watch the
AMS website at www.ams.org/meetings/sectional/
sectional.html for additional information about this
meeting. Please visit the College of Charleston website
cofc.edu for additional information about the campus.
Parking
Conference attendees driving to campus should park in
the St. Philip Street Garage located at 89 St Philip Street,
Charleston, SC 29403. The cost of parking is $1 per half
hour or portion thereof up to $16 per day. Conference attendees
can obtain a day pass at registration that reduces
the daily fee to $10 per day, provided they exit the garage
by 8pm on Friday and Saturday.
Information about parking in downtown Charleston can be
found here: charleston-sc.gov/index.aspx?NID=1025.
Travel
The College of Charleston is located in historic downtown
Charleston, South Carolina.
By Air: The Charleston International Airport is served by
most major airlines. Please visit the Charleston International
Airport web site for a list of airlines serving Charleston
and lists of cities with daily direct flights; iflychs.
com. There are several options available for transportation
to/from the airport. The Charleston Airport shuttle
service offers transportation to downtown Charleston.
The cost is $14 one way. Taxi service from the airport
costs about $30 to downtown Charleston. Information
for ground transportation from the airport can be found
here: www.iflychs.com/Ground-Transportation/
Taxis-Shuttles.aspx.
Rental cars are available at the aiport; for more details
please visit iflychs.com/Ground-Transportation/
Rental-Cars.aspxhttp.
By Train: Charleston is accessible by train via Amtrak to
the North Charleston Station, 4565 Gaynor Avenue which
January 2017 Notices of the AMS 83

MEETINGS & CONFERENCES
is approximately 10 miles from the campus of the College
of Charleston. Routes and schedules can be obtained at
amtrak.com/servlet/ContentServer?pagename=am/
am2Station/Station_Page&code=CHS.
By Bus: Charleston is accessible by bus via Greyhound
to the North Charleston Station, 3610 Dorchester Rd which
is approximately 6.5 miles from the campus of the College
of Charleston. Routes and schedules can be found at
greyhound.com.
By Car:
From Charleston International Airport:
Take I-26 exit. Follow I-26 until it turns into Highway 17.
From Highway 17, take the Meeting St. exit. Follow Meeting
St. several blocks to Calhoun St. Take a right onto Calhoun
St. Follow for two blocks to St. Philip St. Turn right onto St.
Philip St. and the parking garage will be on the left about
half way up the block (89 St. Philip St).
From I-26:
From I-26, take the Meeting St. exit and turn right onto
Meeting St. Follow Meeting St. several blocks to Calhoun
St. Take a right onto Calhoun St. Follow for two blocks to
St. Philip St. Turn right onto St. Philip St. and the parking
garage will be on the left about half way up the block (89
St. Philip St).
From Highway 17N:
Follow Highway 17 over the Ravenel Bridge. Take the
Meeting St. exit. Turn left onto Meeting St. Follow Meeting
St. several blocks to Calhoun St. Take a right at Calhoun
St. Follow for two blocks to St. Philip Street. Turn right
onto St. Philip St. and the parking garage will be on the
left about half way up the block (89 St. Philip St).
From Highway 17S:
From Highway 17, take the Lockwood Dr. exit to the
right. From Lockwood Dr., turn left onto Calhoun St. Follow
Calhoun St. approximately 10 blocks to St. Philip St.
Turn right onto St. Philip St. and the parking garage will
be on the left about half way up the block (89 St. Philip St).
Car Rental: Hertz is the official car rental company for
the meeting. To make a reservation accessing our special
meeting rates online at www.hertz.com, click on the box
"I have a discount," and type in our convention number
(CV): CV#04N30007. You can also call Hertz directly at
800-654-2240 (US and Canada) or 1-405-749-4434 (other
countries). At the time of reservation, the meeting rates
will be automatically compared to other Hertz rates and
you will be quoted the best comparable rate available.
For directions to campus, inquire at your rental car
counter.
Local Transportation
Information for Charleston's local bus service can
be found here: ridecarta.com. Local bus options
are somewhat limited on the weekends, however, CARTA
operates a downtown-area shuttle (DASH Trolley)
that is free: www.ridecarta.com/riding-carta/
routesmapsschedules/carta-dash-trolley-maptimes.
There are several taxi companies in the area, including
Charleston Green Taxi (www.charlestongreentaxi.
com/), Yellow Cab of Charleston (www.yellowcabofcharleston.com/Yellow_Cab_of_Charleston/Home.
html), and Charleston Cab Company (charlestoncabcompany.com/).
However, perhaps the best local option for
individual transport is Uber, as it operates in Charleston
and is very popular.
Weather:
Charleston tends to be cool and mild in March. Daytime
temperatures are in the mid 60s and evening temperatures
are in the mid 40s. Visitors should be prepared for
inclement weather and check weather forecasts in advance
of their arrival.
Social Networking:
Attendees and speakers are encouraged to tweet about
the meeting using the hashtags #AMSmtg.
Information for International Participants:
Visa regulations are continually changing for travel to
the United States. Visa applications may take from three to
four months to process and require a personal interview,
as well as specific personal information. International
participants should view the important information
about traveling to the US found at travel.state.gov/
content/visas/english.html and travel.state.
gov/content/visas/english/general/all-visacategories.html.
If you need a preliminary conference
invitation in order to secure a visa, please send your request
to epm@ams.org.
If you discover you do need a visa, the National Academies
website (see above) provides these tips for successful
visa applications:
* Visa applicants are expected to provide evidence that
they are intending to return to their country of residence.
Therefore, applicants should provide proof of “binding”
or sufficient ties to their home country or permanent
residence abroad. This may include documentation of
the following:
- family ties in home country or country of legal permanent
residence
- property ownership
- bank accounts
- employment contract or statement from employer
stating that the position will continue when the employee
returns;
* Visa applications are more likely to be successful if
done in a visitor's home country than in a third country;
* Applicants should present their entire trip itinerary,
including travel to any countries other than the United
States, at the time of their visa application;
* Include a letter of invitation from the meeting organizer
or the US host, specifying the subject, location and
dates of the activity, and how travel and local expenses
will be covered;
* If travel plans will depend on early approval of the
visa application, specify this at the time of the application;
84 Notices of the AMS Volume 64, Number 1

MEETINGS & CONFERENCES
* Provide proof of professional scientific and/or
educational status (students should provide a university
transcript).
This list is not to be considered complete. Please visit
the websites listed for the most up-to-date information.
Bloomington, Indiana
Indiana University
April 1–2, 2017
Saturday – Sunday
Meeting #1127
Central Section
Associate secretary: Georgia Benkart
Announcement issue of Notices: February 2017
Program first available on AMS website: February 23, 2017
Issue of Abstracts: Volume 38, Issue 2
Deadlines
For organizers: Expired
For abstracts: February 7, 2017
The scientific information listed below may be dated.
For the latest information, see www.ams.org/amsmtgs/
sectional.html.
Invited Addresses
Ciprian Demeter, Indiana University, Title to be announced.
Sarah Koch, University of Michigan, Title to be announced.
Richard Evan Schwartz, Brown University, Modern
scratch paper: Graphical explorations in geometry and dynamics
(12th AMS Einstein Public Lecture in Mathematics).
Special Sessions
If you are volunteering to speak in a Special Session, you
should send your abstract as early as possible via the abstract
submission form found at www.ams.org/cgi-bin/
abstracts/abstract.pl.
Algebraic and Enumerative Combinatorics with Applications
(Code: SS 6A), Saúl A. Blanco, Indiana University, and
Kyle Peterson, DePaul University.
Analysis and Numerical Computations of PDEs in Fluid
Mechanics (Code: SS 20A), Gung-Min Gie, University of
Louisville, and Makram Hamouda and Roger Temam,
Indiana University.
Analysis of Variational Problems and Nonlinear Partial
Differential Equations (Code: SS 11A), Nam Q. Le and Peter
Sternberg, Indiana University.
Automorphic Forms and Algebraic Number Theory
(Code: SS 2A), Patrick B. Allen, University of Illinois at
Urbana-Champaign, and Matthias Strauch, Indiana University
Bloomington.
Commutative Algebra (Code: SS 19A), Ela Celikbas and
Olgur Celikbas, West Virginia University.
Computability and Inductive Definability over Structures
(Code: SS 3A), Siddharth Bhaskar, Lawrence Valby, and
Alex Kruckman, Indiana University.
Dependence in Probability and Statistics (Code: SS 7A),
Richard C. Bradley and Lanh T. Tran, Indiana University.
Differential Equations and Their Applications to Biology
(Code: SS 27A), Changbing Hu, Bingtuan Li, and Jiaxu Li,
University of Louisville.
Discrete Structures in Conformal Dynamics and Geometry
(Code: SS 5A), Sarah Koch, University of Michigan, and
Kevin Pilgrim and Dylan Thurston, Indiana University.
Extremal Problems in Graphs, Hypergraphs and Other
Combinatorial Structures (Code: SS 25A), Amin Bahmanian,
Illinois State University, and Theodore Molla,
University of Illinois Urbana-Champaign.
Financial Mathematics and Statistics (Code: SS 24A),
Ryan Gill, University of Louisville, Rasitha Jayasekera,
Butler University, and Kiseop Lee, Purdue University.
Fusion Categories and Applications (Code: SS 26A), Paul
Bruillard, Pacific Northwest National Laboratory, and Julia
Plavnik and Eric Rowell, Texas A&M University.
Harmonic Analysis and Partial Differential Equations
(Code: SS 9A), Lucas Chaffee, Western Washington University,
William Green, Rose-Hulman Institute of Technology,
and Jarod Hart, University of Kansas.
Homotopy Theory (Code: SS 12A), David Gepner,
Purdue University, Ayelet Lindenstrauss and Michael
Mandell, Indiana University, and Daniel Ramras, Indiana
University-Purdue University Indianapolis.
Model Theory (Code: SS 14A), Gabriel Conant, University
of Notre Dame, and Philipp Hieronymi, University of
Illinois Urbana Champaign.
Multivariate Operator Theory and Function Theory
(Code: SS 21A), Hari Bercovici, Indiana University, Kelly
Bickel, Bucknell University, Constanze Liaw, Baylor University,
and Alan Sola, Stockholm University.
Network Theory (Code: SS 8A), Jeremy Alm and
Keenan M.L. Mack, Illinois College.
Nonlinear Elliptic and Parabolic Partial Differential
Equations and Their Various Applications (Code: SS 13A),
Changyou Wang, Purdue University, and Yifeng Yu, University
of California, Irvine.
Probabilistic Methods in Combinatorics (Code: SS 22A),
Patrick Bennett and Andrzej Dudek, Western Michigan
University.
Probability and Applications (Code: SS 16A), Russell
Lyons and Nick Travers, Indiana University.
Randomness in Complex Geometry (Code: SS 1A), Turgay
Bayraktar, Syracuse University, and Norman Levenberg,
Indiana University.
Representation Stability and its Applications (Code: SS
23A), Patricia Hersh, North Carolina State University,
Jeremy Miller, Purdue University, and Andrew Putman,
University of Notre Dame.
Representation Theory and Integrable Systems (Code:
SS 18A), Eugene Mukhin, Indiana University,Purdue
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MEETINGS & CONFERENCES
University Indianapolis, and Vitaly Tarasov, Indiana University,
Purdue University Indianapolis.
Self-similarity and Long-range Dependence in Stochastic
Processes (Code: SS 10A), Takashi Owada, Purdue University,
Yi Shen, University of Waterloo, and Yizao Wang,
University of Cincinnati.
Spectrum of the Laplacian on Domains and Manifolds
(Code: SS 4A), Chris Judge and Sugata Mondal, Indiana
University.
Topics in Extremal, Probabilistic and Structural Graph
Theory (Code: SS 15A), John Engbers, Marquette University,
and David Galvin, University of Notre Dame.
Topological Mathematical Physics (Code: SS 17A),
E. Birgit Kaufmann and Ralph M. Kaufmann, Purdue University,
and Emil Prodan, Yeshiva University.
Pullman, Washington
Washington State University
April 22–23, 2017
Saturday – Sunday
Meeting #1128
Western Section
Associate secretary: Michel L. Lapidus
Announcement issue of Notices: February 2017
Program first available on AMS website: March 9, 2017
Issue of Abstracts: Volume 38, Issue 2
Deadlines
For organizers: Expired
For abstracts: February 28, 2017
The scientific information listed below may be dated.
For the latest information, see www.ams.org/amsmtgs/
sectional.html.
Invited Addresses
Michael Hitrik, University of California, Los Angeles,
Spectra for non-self-adjoint operators and integrable dynamics.
Andrew S. Raich, University of Arkansas, Title to be
announced.
Daniel Rogalski, University of California, San Diego,
Title to be announced.
Special Sessions
If you are volunteering to speak in a Special Session, you
should send your abstract as early as possible via the abstract
submission form found at www.ams.org/cgi-bin/
abstracts/abstract.pl.
Analysis on the Navier-Stokes equations and related
PDEs (Code: SS 9A), Kazuo Yamazaki, University of
Rochester, and Litzheng Tao, University of California,
Riverside.
Clustering of Graphs: Theory and Practice (Code: SS
18A), Stephen J. Young and Jennifer Webster, Pacific
Northwest National Laboratory.
Combinatorial and Algebraic Structures in Knot Theory
(Code: SS 5A), Sam Nelson, McKenna College, and Allison
Henrich, Seattle University.
Combinatorial and Computational Commutative Algebra
and Algebraic Geometry (Code: SS 21A), Hirotachi
Abo, Stefan Tohaneanu, and Alexander Woo, University
of Idaho.
Commutative Algebra (Code: SS 3A), Jason Lutz and
Katharine Shultis, Gonzaga University.
Fixed Point Methods in Differential and Integral Equations
(Code: SS 1A), Theodore A. Burton, Southern Illinois
University in Carbondale.
Geometric Measure Theory and it’s Applications (Code:
SS 20A), .
Geometry and Optimization in Computer Vision (Code:
SS 15A), Bala Krishnamoorthy, Washington State University,
and Sudipta Sinha, Microsoft Research, Redmond,
WA.
Inverse Problems (Code: SS 2A), Hanna Makaruk, Los
Alamos National Laboratory (LANL), and Robert Owczarek,
University of New Mexico, Albuquerque & Los Alamos.
Mathematical & Computational Neuroscience (Code: SS
12A), Alexander Dimitrov, Washington State University
Vancouver, Andrew Oster, Eastern Washington University,
and Predrag Tosic, Washington State University.
Mathematical Modeling of Forest and Landscape Change
(Code: SS 11A), Nikolay Strigul and Jean Lienard, Washington
State University Vancouver.
Microlocal Analysis and Spectral Theory (Code: SS 17A),
Michael Hitrik, University of California, Los Angeles, and
Semyon Dyatlov, Masssachusetts Institute of Technology.
Noncommutative algebraic geometry and related topics
(Code: SS 16A), Daniel Rogalski, University of California,
San Diego, and James Zhang, University of Washington.
Partial Differential Equations and Applications (Code:
SS 8A), V. S. Manoranjan, C. Moore, Lynn Schreyer, and
Hong-Ming Yin, Washington State University.
Recent Advances in Applied Algebraic Topology (Code:
SS 14A), Henry Adams, Colorado State University, and
Bala Krishnamoorthy, Washington State University.
Recent Advances in Optimization and Statistical Learning
(Code: SS 19A), Hongbo Dong, Bala Krishnamoorthy,
Haijun Li, and Robert Mifflin, Washington State University.
Recent Advances on Mathematical Biology and Their
Applications (Code: SS 7A), Robert Dillon and Xueying
Wang, Washington State University.
Several Complex Variables and PDEs (Code: SS 10A),
Andrew Raich and Phillip Harrington, University of
Arkansas.
Special Session on Analytic Number Theory and Automorphic
Forms (Code: SS 6A), Steven J. Miller, Williams
College, and Sheng-Chi Liu, Washington State University.
86 Notices of the AMS Volume 64, Number 1

MEETINGS & CONFERENCES
Theory and Applications of Linear Algebra (Code: SS
4A), Judi McDonald and Michael Tsatsomeros, Washington
State University.
Undergraduate Research Experiences in the Classroom
(Code: SS 13A), Heather Moon, Lewis-Clark State College.
New York, New York
Hunter College, City University of New
York
May 6–7, 2017
Saturday – Sunday
Meeting #1129
Eastern Section
Associate secretary: Steven H. Weintraub
Announcement issue of Notices: March 2017
Program first available on AMS website: March 22, 2017
Issue of Abstracts: Volume 38, Issue 2
Deadlines
For organizers: Expired
For abstracts: March 14, 2017
The scientific information listed below may be dated.
For the latest information, see www.ams.org/amsmtgs/
sectional.html.
Invited Addresses
Jeremy Kahn, City University of New York, Title to be
announced.
Fernando Coda Marques, Princeton University, Title to
be announced.
James Maynard, Magdalen College, University of Oxford,
Title to be announced (Erdős Memorial Lecture).
Kavita Ramanan, Brown University, Title to be announced.
Special Sessions
If you are volunteering to speak in a Special Session, you
should send your abstract as early as possible via the abstract
submission form found at www.ams.org/cgi-bin/
abstracts/abstract.pl.
Analysis and numerics on liquid crystals and soft matter
(Code: SS 16A), Xiang Xu, Old Dominion University, and
Wujun Zhang, Rutgers University.
Applications of network analysis, in honor of Charlie
Suffel’s 75th birthday (Code: SS 18A), Michael Yatauro,
Pennsylvania State University-Brandywine.
Banach Space Theory and Metric Embeddings (Code: SS
10A), Mikhail Ostrovskii, St John’s University, and Beata
Randrianantoanina, Miami University of Ohio.
Cluster Algebras in Representation Theory and Combinatorics
(Code: SS 6A), Alexander Garver, Université
du Quebéc à Montréal and Sherbrooke, and Khrystyna
Serhiyenko, University of California at Berkeley.
Cohomologies and Combinatorics (Code: SS 15A), Rebecca
Patrias, Université du Québec à Montréal, and Oliver
Pechenik, Rutgers University.
Common Threads to Nonlinear Elliptic Equations and
Systems (Code: SS 14A), Florin Catrina, St. John’s University,
and Wenxiong Chen, Yeshiva University.
Commutative Algebra (Code: SS 1A), Laura Ghezzi,
New York City College of Technology-CUNY, and Jooyoun
Hong, Southern Connecticut State University.
Computability Theory: Pushing the Boundaries (Code:
SS 9A), Johanna Franklin, Hofstra University, and Russell
Miller, Queens College and Graduate Center, City University
of New York.
Computational and Algorithmic Group Theory (Code:
SS 7A), Denis Serbin and Alexander Ushakov, Stevens
Institute of Technology.
Cryptography (Code: SS 3A), Xiaowen Zhang, College
of Staten Island and Graduate Center-CUNY.
Current Trends in Function Spaces and Nonlinear Analysis
(Code: SS 2A), David Cruz-Uribe, University of Alabama,
Jan Lang, The Ohio State University, and Osvaldo Mendez,
University of Texas at El Paso.
Differential and Difference Algebra: Recent Developments,
Applications, and Interactions (Code: SS 12A), Omár
León-Sanchez, McMaster University, and Alexander Levin,
The Catholic University of America.
Geometric Function Theory and Related Topics (Code: SS
19A), Sudeb Mitra, Queens College and Graduate Center-
CUNY, and Zhe Wang, Bronx Community College-CUNY.
Geometry and Topology of Ball Quotients and Related
Topics (Code: SS 5A), Luca F. Di Cerbo, Max Planck Institute,
Bonn, and Matthew Stover, Temple University.
Hydrodynamic and Wave Turbulence (Code: SS 11A),
Tristan Buckmaster, Courant Institute of Mathematical
Sciences, New York University, and Vlad Vicol, Princeton
University.
Infinite Permutation Groups, Totally Disconnected Locally
Compact Groups, and Geometric Group Theory (Code:
SS 4A), Delaram Kahrobaei, New York City College of
Technology and Graduate Center-CUNY, and Simon Smith,
New York City College of Technology-CUNY.
Nonlinear and Stochastic Partial Differential Equations:
Theory and Applications in Turbulence and Geophysical
Flows (Code: SS 8A), Nathan Glatt-Holtz, Tulane University,
Geordie Richards, Utah State University, and Xiaoming
Wang, Florida State University.
Operator algebras and ergodic theory (Code: SS 17A),
Genady Grabarnik and Alexander Katz, St John’s University.
Qualitative and Quantitative Properties of Solutions to
Partial Differential Equations (Code: SS 20A), Blair Davey,
The City College of New York-CUNY, and Nguyen Cong
Phuc and Jiuyi Zhu, Louisiana State University.
Recent Developments in Automorphic Forms and Representation
Theory (Code: SS 21A), Moshe Adrian, Queens
January 2017 Notices of the AMS 87

MEETINGS & CONFERENCES
College-CUNY, and Shuichiro Takeda, University of Missouri.
Representation Spaces and Toric Topology (Code: SS
13A), Anthony Bahri, Rider University, and Daniel Ramras
and Mentor Stafa, Indiana University-Purdue University
Indianapolis.
Montréal, Quebec
Canada
McGill University
July 24–28, 2017
Monday – Friday
Meeting #1130
The second Mathematical Congress of the Americas (MCA
2017) is being hosted by the Canadian Mathematical Society
(CMS) in collaboration with the Pacific Institute for the
Mathematical Sciences (PIMS), the Fields Institute (FIELDS),
Le Centre de Recherches Mathématiques (CRM), and the
Atlantic Association for Research in the Mathematical Sciences
(AARMS).
Associate secretary: Brian D. Boe
Announcement issue of Notices: January
Program first available on AMS website: January 23, 2016
Deadlines
For organizers: Expired
For abstracts: March 31, 2017
This announcement was composed with information taken
from the website maintained by the local organizers at
mca2017.org. Please watch this website for the most upto-date
information.
Accommodations
Preferred rates with a number of accommodation sites
have been negotiated for the Congress. Please mention the
Mathematical Congress of the Americas and the Canadian
Mathematical Society when reserving your room. Most of
the congress will be happening either at McGill University
or just opposite at the Centre Mont-Royal. All of the
hotels with preferred rates are within walking distance of
the venues. A map can be found at mca2017.org/
accommodation. All rates are subject to applicable fees
and taxes (currently 14.975 percent in the province of
Quebec). All rates listed in this announcement are in
Canadian dollars (CAD), unless otherwise noted.
Marriott Chateau Champlain, 1 Place du Canada, Montreal,
Quebec, Canada H3B 4C9 (1.0km to Centre Mont-Royal)
Phone: 1-514-878-9000; Toll Free: 1-800-200-5909; Rate:
$149.00/night* for Standard Deluxe Non-Smoking Room.
Smoke-free rooms; Complimentary wired and wireless
high-speed internet; Business centre; Indoor pool; Health
and Fitness centre; Hair Salon; Lobby level shops and
boutiques; Bank machine; Laundry services; In-room
safety boxes; Self-parking $23/24 hours (without in and
out privileges); Daily valet parking $32 (max. clearance
1.83m); Babysitting services available; On-site restaurant:
Samuel de Champlain; On-site bar: Le Bar Senateur; Starbucks
Coffee on-site.
Le Meridien Versailles 1808 Rue Sherbrooke Ouest,
Montreal, Quebec, Canada H3H 1E5 (1.0km to Centre
Mont-Royal) Phone: 1-514-933-8111; Central Reservations:
1-888-627-8151; Rate: $149.00/night* for a variety of
room styles; Complimentary wireless high-speed internet;
Business Centre; Health Club; Laundry and dry cleaning
service; Safe deposit boxes; In-room Safe; Valet service (at
additional charge); Wake-up service; Turn-down service;
International Direct Dialing; Voicemail; Childcare service
(at additional cost); Pets welcome ($15/day); Currency exchange
from USD to CAD (max. of $100); 24 hour Doctor
on-call (at additional charge); On-site restaurant: Branzino
Restaurant Montreal.
New Residence Hall (McGill) 3625 Avenue du Parc, Montreal,
Quebec, Canada H2X 3P8 (1.1km to Centre Mont-
Royal) Phone : 514-398-5200; Rate: $99/night* (2015 rate,
subject to change); Hotel-style residence; Complimentary
wireless internet; business centre; underground shopping
centre: Galleries du Parc; gym with outdoor pool located in
shopping centre at reduced rate; laundry room open 24/7
(at additional charge); daily housekeeping; individual air
conditioning control; cable TV; Private bathroom; Children
12 and under sleep for free in existing room bedding; Onsite
self-parking at ~$20/day (taxes included).
Royal Victoria College Traditional Residence (McGill)
845 Rue Sherbrooke Ouest, Montreal, Quebec, Canda H3A
0G4 (0.1km from Centre Mont-Royal) Phone: 514-398-
5200; Rate: $49/night* (2015 rate, subject to change).
Traditional single room residence accommodation; sheets,
towels and soap provided; residence lounge, study room
and TV room; laundry facilities (card-operated at additional
cost); public telephones; communal kitchen for
cooking (a limited number of utensils/pots/pans are
available on loan from the front desk).
La Catadel (McGill) 410 Rue Sherbrooke Ouest, Montreal,
Quebec, Canada H3A 1B3 (0.6km from Centre Mont-Royal);
Phone: 514-398-5200; Rate: $119/night* (2015 rate, subject
to change); Hotel-style residence; Construction completed
in 2012; Complimentary wireless internet; cable
TV; Small fridge; individual air-conditioning; Residence
common room; Residence study room; Communal kitchen;
Laundry facilities (card-operated at additional cost).
Carrefour Sherbrooke (McGill) 475 Rue Sherbrooke Ouest,
Montreal, Quebec, Canada H3A 2L9(0.5km from Centre
Mont-Royal); Phone: 514-398-5200; Rate: $119/night*
(2015 rate, subject to change); Hotel-style residence; Complimentary
wireless internet; Fitness centre; individual air
conditioning; cable TV; Small refrigerator; Private washroom;
Daily housekeeping; Laundry facilities (at additional
cost); Children 12 and under sleep free in existing room
bedding; off-site self-parking at ~$25/day + taxes.
88 Notices of the AMS Volume 64, Number 1

MEETINGS & CONFERENCES
Food Services and Dining
The conference is being held in downtown Montreal,
with a large number of office workers and students stepping
out at noon for lunch; there is a wide variety of places
along McGill College Avenue and Rue Ste-Catherine. The
office buildings for example, tend to have food courts,
with some of the ‘ethnic’ counters in them (Thai, Vietnamese,
Lebanese…) serving quite decent food. A map
can be found below.
The area around McGill is rather short on higher end
restaurants but if you go a bit further afield you will be
well served. There is, naturally, a certain emphasis on
French cooking, but as for any large North American city,
you will find cuisine from all around the world.
A useful and fairly reliable guide, in french, is guiderestos.com/montreal/.
Registration and Meeting Information
Advance Registration
Online registration will open closer to the dates of the
program and close on June 30, 2017. Registration fees will
be posted closer to the dates of the program. Please visit
mca2017.org for registration.
On-site Registration
On-site registration will be available beginning Sunday,
July 23, 2017.
Other Activities
The Congress has arranged a special evening concert by
the Cecilia String Quartet as an optional event on Tuesday
July 25th in Pollack Hall at McGill University. Each ticket
costs $10 USD or $ 13 CAD.
A formal banquet will be held on Thursday, July 27. Details,
to be announced. mca2017.org/fees-deadlines/.
The AMS thanks our hosts for their gracious hospitality.
Local Information and Maps
The primary venues for MCA 2017 will be the Centre Mont-
Royal and McGill University. Some council and committee
meetings will also be convened at the Montreal Marriott
Chateau Champlain.
All venues are located in downtown Montreal within walking
distance of each other.
Shuttle transportation will also be provided throughout
the congress to assist participants with mobility challenges.
For more information about the MCA´s venues, please
visit: mca2017.org/travel/venues.
Travel
By Air: You will no doubt be arriving in Canada either
through the Montreal or Toronto airports. You will be required
to clear Canadian customs at your port of arrival,
so please leave enough time between, say, an arrival in
Toronto and a departure for Montreal. Many flights from
South America involve transit through the US, which often
requires a US travel document.
Once you have arrived at Trudeau airport in Montreal, the
options for getting downtown are:
Taxi ($40 flat rate, with a 10-15 percent tip being customary)
Bus (appropriately, number 747) that goes every ten
minutes or so during the day. Featuring 24-hour service,
7 days a week, 365-days a year. The route features nine
downtown stops conveniently located near major hotels
and takes approximately 25–30 minutes each way, depending
on traffic. The stop closest to the conference venue is
René-Lévesque-Mansfield.
Car rental and limousine transportation companies are on
site as well as airport shuttles
Air Canada is the Official Canadian Airline for this event,
offering special discounts to delegates attending the 2017
Mathematical Congress of the Americas for travel to and
from Montreal, YUL (QC) between July 16 and August 5,
2017. The Promotion Code DTYY2V81 has to be entered
during the booking. If it is not entered or entered incorrectly,
the discounts will not be applied to the booking.
Ticketing agencies/airlines must record the code on the
delegate's ticket.
Discounts: 10 percent discount on most fares, but no
discount will apply to Tango bookings for travel within
Canada or between Canada and the US. Note that promotional
codes apply to undiscounted published fares. Some
of Air Canada's previously discounted fares, while not eligible
for the promotion, may be lower than the final price
of the undiscounted fare to which the promotion applies.
By Train: VIA Rail Canada serves more than 450 Canadian
cities. If you are coming from the United States, hop
aboard an Amtrak train, with daily departures from several
American cities to downtown Montréal. Visitors pull into
Montréal’s Central Station, which is conveniently linked to
the Underground Pedestrian Network and the Bonaventure
metro station.
By Bus: If you are planning a trip by bus, many
American and Canadian operators come to Montréal,
including Orléans Express. You will arrive directly
downtown at the Montréal Bus Central Station,
which is also connected to the Underground
Pedestrian Network via the Berri-UQAM metro station.
Weather
Montreal tends to be warm in July. Daytime temperatures
are in the mid 80s and evening temperatures are in
the mid 60s. Visitors should be prepared for inclement
weather and check weather forecasts in advance of their
arrival. For more information please visit: tourismemontreal.org.
January 2017 Notices of the AMS 89

MEETINGS & CONFERENCES
Information for International Participants:
Visas-travelling to Canada
You will need to have appropriate travel documents
if you are coming to Canada. The official requirements
can vary in time, please consult the Government of
Canada's web site: www.cic.gc.ca/english/visit. We
can provide you with a letter of invitation: as you register,
please check the appropriate box and fill in the required
information. Once payment has been received a letter will
be mailed or e-mailed to you.
If you are not sure if you require an Electronic Travel
Authorization (ETA) or a visitor VISA, please click here.
Choose your country to find out what you require to travel
to Canada.
Note that a new entry requirement is now in effect:
visa-exempt foreign nationals need an ETA to fly to or
transit through Canada. Exceptions include US citizens,
and travellers with a valid Canadian visa. Canadian citizens,
including dual citizens, and Canadian permanent
residents need not apply for an ETA.
As an indication:
US citizens: In essence, the only travel document required
is a valid passport, both for getting into Canada,
and for returning to your country afterwards.
Mexican citizens: Here the situation is in flux. A visa
requirement was imposed a few years ago, Starting December
1, 2016, you will need an Electronic Travel Authorization
(eTA) to travel to or transit through Canada.
However, please check here to ensure this information is
still correct.
The rest of the Americas: Citizens of most of the
countries of the Americas require visas; the Government
of Canada web site does not provide a list, but you can
check your country here. Even if no Visa is required, an
Electronic Travel Authorization (eTA) might be necessary:
the status of this requirement is also in flux.
The rest of the World: Please consult the web site.
Again, even if you are from a country like Britain or France,
for which we do not require a visa, an Electronic Travel
Authorization (eTA) is necessary at this time.
Invitation Letters
The MCA wish to support international attendees in
their efforts to secure the needed travel documentation.
However, in order to receive a letter of invitation, the
meeting organizers must be assured that you intend to
attend the meeting if your travel request is granted. Individuals
that require an official letter of invitation in order
to obtain a visa and authorization to attend the meeting
must register for the congress and request a Visa Letter
of Invitation during their registration process.
The letter of invitation does not financially obligate the
organizers in any way. All expenses incurred in relation to
the conference are the sole responsibility of the attendee.
Please note that we cannot guarantee that you will receive
a visa. The decision to grant visas is at the sole discretion
of the embassy/consulate. The conference organizers
cannot change the decision of the governmental agency
should your application be denied.
Advance travel planning and early visa application are
important. It is recommended that you apply early for
your visa.
Denton, Texas
University of North Texas
September 9–10, 2017
Saturday – Sunday
Meeting #1131
Central Section
Associate secretary: Georgia Benkart
Announcement issue of Notices: June 2017
Program first available on AMS website: July 27, 2017
Issue of Abstracts: Volume 38, Issue 3
Deadlines
For organizers: February 2, 2017
For abstracts: July 18, 2017
The scientific information listed below may be dated.
For the latest information, see www.ams.org/amsmtgs/
sectional.html.
Invited Addresses
Mirela Çiperiani, University of Texas at Austin, Title
to be announced.
Adrianna Gillman, Rice University, Title to be announced.
Kevin Pilgrim, Indiana University, Title to be announced.
Special Sessions
If you are volunteering to speak in a Special Session, you
should send your abstract as early as possible via the abstract
submission form found at www.ams.org/cgi-bin/
abstracts/abstract.pl.
Banach Spaces and Applications (Code: SS 9A), Pavlos
Motakis, Texas A&M University, and Bönyamin Sari, University
of North Texas.
Differential Equation Modeling and Analysis for Complex
Bio-systems (Code: SS 8A), Pengcheng Xiao, University of
Evansville, and Honghui Zhang, Northwestern Polytechnical
University.
Dynamics, Geometry and Number Theory (Code: SS
1A), Lior Fishman and Mariusz Urbanski, University of
North Texas.
Fractal Geometry and Ergodic Theory (Code: SS 5A),
Mrinal Kanti Roychowdhury, University of Texas Rio
Grande Valley.
Invariants of Links and 3-Manifolds (Code: SS 7A), Mieczyslaw
K. Dabkowski and Anh T. Tran, The University
of Texas at Dallas.
90 Notices of the AMS Volume 64, Number 1

MEETINGS & CONFERENCES
Lie algebras, Superalgebras, and Applications (Code: SS
3A), Charles H. Conley, University of North Texas, and
Dimitar Grantcharov, University of Texas at Arlington.
Noncommutative and Homological Algebra (Code: SS
4A), Anne Shepler, University of North Texas, and Sarah
Witherspoon, Texas A&M University.
Numbers, Functions, Transcendence, and Geometry
(Code: SS 6A), William Cherry, University of North Texas,
Mirela Çiperiani, University of Texas Austin, Matt Papanikolas,
Texas A&M University, and Min Ru, University
of Houston.
Real-Analytic Automorphic Forms (Code: SS 2A), Olav K
Richter, University of North Texas, and Martin Westerholt-
Raum, Chalmers University of Technology.
Buffalo, New York
State University of New York at Buffalo
September 16–17, 2017
Saturday – Sunday
Orlando, Florida
University of Central Florida, Orlando
September 23–24, 2017
Saturday – Sunday
Meeting #1133
Southeastern Section
Associate secretary: Brian D. Boe
Announcement issue of Notices: June 2017
Program first available on AMS website: August 10, 2017
Issue of Abstracts: Volume 38, Issue 4
Deadlines
For organizers: February 23, 2017
For abstracts: August 1, 2017
The scientific information listed below may be dated.
For the latest information, see www.ams.org/amsmtgs/
sectional.html.
Meeting #1132
Eastern Section
Associate secretary: Steven H. Weintraub
Announcement issue of Notices: June 2017
Program first available on AMS website: August 3, 2017
Issue of Abstracts: Volume 38, Issue 3
Deadlines
For organizers: February 16, 2017
For abstracts: July 25, 2017
The scientific information listed below may be dated.
For the latest information, see www.ams.org/amsmtgs/
sectional.html.
Invited Addresses
Inwon Kim, University of California at Los Angeles,
Title to be announced.
Govind Menon, Brown University, Title to be announced.
Bruce Sagan, Michigan State University, Title to be announced.
Special Sessions
If you are volunteering to speak in a Special Session, you
should send your abstract as early as possible via the abstract
submission form found at www.ams.org/cgi-bin/
abstracts/abstract.pl.
Nonlinear Wave Equations, inverse scattering and applications.
(Code: SS 1A), Gino Biondini, University at
Buffalo-SUNY.
Invited Addresses
Christine Heitsch, Georgia Institute of Technology,
Title to be announced.
Jonathan Kujawa, University of Oklahoma, Title to be
announced.
Christopher D Sogge, Johns Hopkins University, Title
to be announced.
Special Sessions
If you are volunteering to speak in a Special Session, you
should send your abstract as early as possible via the abstract
submission form found at www.ams.org/cgi-bin/
abstracts/abstract.pl.
Algebraic Curves and their Applications (Code: SS 3A),
Lubjana Beshaj, The University of Texas at Austin.
Applied Harmonic Analysis: Frames, Samplings and
Applications (Code: SS 6A), Dorin Dutkay, Deguang Han,
and Qiyu Sun, University of Central Florida.
Commutative Algebra: Interactions with Algebraic
Geometry and Algebraic Topology (Code: SS 1A), Joseph
Brennan, University of Central Florida, and Alina Iacob
and Saeed Nasseh, Georgia Southern University.
Fractal Geometry, Dynamical Systems, and Their Applications
(Code: SS 4A), Mrinal Kanti Roychowdhury,
University of Texas Rio Grande Valley.
Graph Connectivity and Edge Coloring (Code: SS 5A),
Colton Magnant, Georgia Southern University.
Structural Graph Theory (Code: SS 2A), Zixia Song,
University of Central Florida.
January 2017 Notices of the AMS 91

MEETINGS & CONFERENCES
Riverside, California
University of California, Riverside
November 4–5, 2017
Saturday – Sunday
Meeting #1134
Western Section
Associate secretary: Michel L. Lapidus
Announcement issue of Notices: September 2017
Program first available on AMS website: September 21,
2017
Issue of Abstracts: Volume 38, Issue 4
Deadlines
For organizers: April 14, 2017
For abstracts: September 12, 2017
The scientific information listed below may be dated.
For the latest information, see www.ams.org/amsmtgs/
sectional.html.
Invited Addresses
Paul Balmer, University of California, Los Angeles, Title
to be announced.
Pavel Etingof, Massachusetts Institute of Technology,
Title to be announced.
Monica Vazirani, University of California, Davi, Title
to be announced.
Special Sessions
If you are volunteering to speak in a Special Session, you
should send your abstract as early as possible via the abstract
submission form found at www.ams.org/cgi-bin/
abstracts/abstract.pl.
Combinatorial aspects of the polynomial ring (Code:
SS 1A), Sami Assaf and Dominic Searles, University of
Southern California.
Ring Theory and Related Topics (Celebrating the 75th
Birthday of Lance W. Small) (Code: SS 2A), Jason Bell,
University of Waterloo, Ellen Kirkman, Wake Forest University,
and Susan Montgomery, University of Southern
California.
San Diego, California
San Diego Convention Center and
San Diego Marriott Hotel and Marina
January 10–13, 2018
Wednesday – Saturday
Meeting #1135
Joint Mathematics Meetings, including the 124th Annual
Meeting of the AMS, 101st Annual Meeting of the
Mathematical Association of America (MAA), annual meetings
of the Association for Women in Mathematics (AWM)
and the National Association of Mathematicians (NAM),
and the winter meeting of the Association of Symbolic Logic
(ASL), with sessions contributed by the Society for Industrial
and Applied Mathematics (SIAM).
Associate secretary: Georgia Benkart
Announcement issue of Notices: October 2017
Program first available on AMS website: To be announced
Issue of Abstracts: Volume 39, Issue 1
Deadlines
For organizers: April 1, 2017
For abstracts: To be announced
Columbus, Ohio
Ohio State University
March 17–18, 2018
Saturday – Sunday
Meeting #1136
Central Section
Associate secretary: Georgia Benkart
Announcement issue of Notices: To be announced
Program first available on AMS website: To be announced
Issue of Abstracts: To be announced
Deadlines
For organizers: To be announced
For abstracts: To be announced
The scientific information listed below may be dated.
For the latest information, see www.ams.org/amsmtgs/
sectional.html.
Special Sessions
If you are volunteering to speak in a Special Session, you
should send your abstract as early as possible via the abstract
submission form found at www.ams.org/cgi-bin/
abstracts/abstract.pl.
Probability in Convexity and Convexity in Probability
(Code: SS 2A), Elizabeth Meckes, Mark Meckes, and Elisabeth
Werner, Case Western Reserve University.
Recent Advances in Approximation Theory and Operator
Theory (Code: SS 1A), Jan Lang and Paul Nevai, The
Ohio State University.
92 Notices of the AMS Volume 64, Number 1

MEETINGS & CONFERENCES
Nashville, Tennessee
Vanderbilt University
April 14–15, 2018
Saturday – Sunday
Meeting #1138
Southeastern Section
Associate secretary: Brian D. Boe
Announcement issue of Notices: To be announced
Program first available on AMS website: To be announced
Issue of Abstracts: To be announced
Deadlines
For organizers: To be announced
For abstracts: To be announced
Portland, Oregon
Portland State University
April 14–15, 2018
Saturday – Sunday
Meeting #1137
Western Section
Associate secretary: Michel L. Lapidus
Announcement issue of Notices: To be announced
Program first available on AMS website: To be announced
Issue of Abstracts: To be announced
Deadlines
For organizers: To be announced
For abstracts: To be announced
The scientific information listed below may be dated.
For the latest information, see www.ams.org/amsmtgs/
sectional.html.
Special Sessions
If you are volunteering to speak in a Special Session, you
should send your abstract as early as possible via the abstract
submission form found at www.ams.org/cgi-bin/
abstracts/abstract.pl.
Inverse Problems (Code: SS 2A), Hanna Makaruk, Los
Alamos National Laboratory (LANL), and Robert Owczarek,
University of New Mexico, Albuquerque & Los Alamos.
Pattern Formation in Crowds, Flocks, and Traffic (Code:
SS 1A), J. J. P. Veerman, Portland State University, Alethea
Barbaro, Case Western Reserve University, and Bassam
Bamieh, UC Santa Barbara.
Boston,
Massachusetts
Northeastern University
April 21–22, 2018
Saturday – Sunday
Meeting #1139
Eastern Section
Associate secretary: Steven H. Weintraub
Announcement issue of Notices: To be announced
Program first available on AMS website: To be announced
Issue of Abstracts: To be announced
Deadlines
For organizers: September 21, 2017
For abstracts: March 6, 2018
Shanghai, People’s
Republic of China
Fudan University
June 11–14, 2018
Monday – Thursday
Meeting #1140
Associate secretary: Steven H. Weintraub
Announcement issue of Notices: To be announced
Program first available on AMS website: To be announced
Issue of Abstracts: To be announced
Deadlines
For organizers: To be announced
For abstracts: To be announced
Newark, Delaware
University of Delaware
September 29–30, 2018
Saturday – Sunday
Eastern Section
Associate secretary: Steven H. Weintraub
Announcement issue of Notices: To be announced
Program first available on AMS website: To be announced
Issue of Abstracts: To be announced
Deadlines
For organizers: February 28, 2018
For abstracts: To be announced
January 2017 Notices of the AMS 93

MEETINGS & CONFERENCES
San Francisco,
California
San Francisco State University
October 27–28, 2018
Saturday – Sunday
Western Section
Associate secretary: Michel L. Lapidus
Announcement issue of Notices: August 2018
Program first available on AMS website: To be announced
Issue of Abstracts: To be announced
Deadlines
For organizers: April 30, 2018
For abstracts: August 28, 2018
Baltimore, Maryland
Baltimore Convention Center, Hilton
Baltimore, and Baltimore Marriott
Inner Harbor Hotel
January 16–19, 2019
Wednesday – Saturday
Joint Mathematics Meetings, including the 125th Annual
Meeting of the AMS, 102nd Annual Meeting of the Mathematical
Association of America (MAA), annual meetings
of the Association for Women in Mathematics (AWM)and
the National Association of Mathematicians (NAM), and the
winter meeting of the Association of Symbolic Logic (ASL),
with sessions contributed by the Society for Industrial and
Applied Mathematics (SIAM).
Associate secretary: Steven H. Weintraub
Announcement issue of Notices: October 2018
Program first available on AMS website: To be announced
Issue of Abstracts: To be announced
Deadlines
For organizers: April 2, 2018
For abstracts: To be announced
Honolulu, Hawaii
University of Hawaii at Manoa
March 29–31, 2019
Friday – Sunday
Central Section
Associate secretaries: Georgia Benkart and Michel L.
Lapidus
Announcement issue of Notices: To be announced
Program first available on AMS website: To be announced
Issue of Abstracts: To be announced
Deadlines
For organizers: To be announced
For abstracts: To be announced
Denver, Colorado
Colorado Convention Center
January 15–18, 2020
Wednesday – Saturday
Joint Mathematics Meetings, including the 126th Annual
Meeting of the AMS, 103rd Annual Meeting of the Mathematical
Association of America (MAA), annual meetings
of the Association for Women in Mathematics (AWM) and
the National Association of Mathematicians (NAM), and the
winter meeting of the Association of Symbolic Logic (ASL),
with sessions contributed by the Society for Industrial and
Applied Mathematics (SIAM)
Associate secretary: Michel L. Lapidus
Announcement issue of Notices: To be announced
Program first available on AMS website: November 1, 2019
Issue of Abstracts: To be announced
Deadlines
For organizers: April 1, 2019
For abstracts: To be announced
Washington, District
of Columbia
Walter E. Washington Convention Center
January 6–9, 2021
Wednesday – Saturday
Joint Mathematics Meetings, including the 127th Annual
Meeting of the AMS, 104th Annual Meeting of the Mathematical
Association of America (MAA), annual meetings
of the Association for Women in Mathematics (AWM) and
the National Association of Mathematicians (NAM), and the
winter meeting of the Association of Symbolic Logic (ASL),
with sessions contributed by the Society for Industrial and
Applied Mathematics (SIAM).
Associate secretary: Brian D. Boe
Announcement issue of Notices: October 2020
Program first available on AMS website: November 1, 2020
Issue of Abstracts: To be announced
Deadlines
For organizers: April 1, 2020
For abstracts: To be announced
94 Notices of the AMS Volume 64, Number 1

American Mathematical Society
100 years from now you can still be
advancing mathematics.
When it’s time to think about your estate plans, consider making a provision
for the American Mathematical Society to extend your dedication to
mathematics well into the future.
Professional staff at the AMS can share ideas on wills, trusts, life insurance
plans, and more to help you achieve your charitable goals.
For more information:
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THE BACK PAGE
The October Contest Winner Is...
Mason Porter, who receives our book award.
The January 2017 Caption Contest:
What's the Caption?
Reprinted artwork by John Joyce;
www.spindriftpress.com.
Tadashi Tokieda
“Cthulhu really enjoyed being a mathematics
PhD student, and he found that he was especially
good at multitasking.”
Submit your entry to captions@ams.org
by January 25. The winning entry will be
posted here in the April 2017 issue.
"Do you know what is the best prize for solving a problem?
That you always get a new problem from it."
—Louis Nirenberg in interview in La Vanguardia
QUESTIONABLE MATHEMATICS
70%
[The] share of students who consider themselves above average in academic ability—a
mathematical impossibility.—"In Praise of the Ordinary Child," Time Magazine, August
3, 2015.
Yet, our reader Michael Levitan shows it is possible: 10, 10, 10, 10, 10, 10, 10, 0, 0, 0
What crazy things happen to you? Readers are invited to submit original short amusing stories, math
jokes, cartoons, and other material to: noti-backpage@ams.org.
96 Notices of the AMS Volume 64, Number 1

NEW!
IN THE NEXT ISSUE OF NOTICES
FEBRUARY 2017…
Daniel Rothman, MIT
Maintaining a
Tipping points are important—and well-nam
of many complex systems, including financial
systems. At a tipping point, a small change in
system can result in drastic changes overall
change in the weight of one end of a see-saw
positions). Most such systems are studied us
mod
colle
diffe
The
equa
lead
in th
pote
chan
econ
Rese
don
tipp
that
be d
too
A cover story on Maryna
Viazovska’s 2016 solution
of the sphere packing
problem in eight
dimensions, which was
promptly followed by a
collaborative proof in
twenty-four dimensions.
Daniel H. Rothman’s
“Mathematical Expression
of a Global
Listen
Environmental
Up!
Catastrophe,” a
Communication article on
mathematical analyses of
the temporal MM/127.s evolution of
geothermal signals.
Maintaining a Balance: A
new Mathematical Moment
about tipping points.
The Mathematical Momen
appreciation and understandin
plays in science, nature, techno
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AMERICAN MATHEMATICAL SOCIETY
The AMS presents a selection of the titles on display at the
MATHEMATICAL
ANALYSIS AND ITS
INHERENT NATURE
Hossein Hosseini Giv,
University of Sistan and
Baluchestan, Zahedan,
Iran
Written in the belief that
emphasizing the inherent
nature of a mathematical discipline helps students
to understand it better, this text is divided
into two parts based on the way they are related
to calculus: completion and abstraction.
Pure and Applied Undergraduate Texts, Volume 25;
2016; 348 pages; Hardcover; ISBN: 978-1-4704-2807-
5; List US$89; AMS members US$71.20; Order code
AMSTEXT/25
S. R. S. VARADHAN
Large
Deviations
27
LARGE
DEVIATIONS
S. R. S. Varadhan, Courant
Institute of Mathematical
Sciences, New York, NY
Based on a graduate course
at the Courant Institute, this
book focuses on three concrete
sets of examples that
are worked out in detail, giving
the reader a flavor of how large deviation
theory can help in problems that are not posed
directly in terms of large deviations.
Titles in this series are co-published with the Courant Institute of
Mathematical Sciences at New York University.
Courant Lecture Notes, Volume 27; 2016; 104 pages;
Softcover; ISBN: 978-0-8218-4086-3; List US$36; AMS
members US$28.80; Order code CLN/27
GRADUATE STUDIE S
IN MATHEMATICS 174
Quiver
Representations
and Quiver
Varieties
Alexander Kirillov Jr.
American Mathematical Society
QUIVER
REPRESENTATIONS
AND QUIVER
VARIETIES
Alexander Kirillov Jr.,
Stony Brook University, NY
This book is an introduction
to the theory of quiver representations
and quiver varieties,
starting with basic definitions and ending
with Nakajima’s work on quiver varieties and
the geometric realization of Kac-Moody algebras.
Graduate Studies in Mathematics, Volume 174; 2016;
295 pages; Hardcover; ISBN: 978-1-4704-2307-0; List
US$89; AMS members US$71.20; Order code GSM/174
THE CASE OF
ACADEMICIAN
NIKOLAI
NIKOLAEVICH
LUZIN
Sergei S. Demidov,
Russian Academy of
Sciences, Moscow, Russia
and Boris V. Lëvshin,
Editors
Translated by Roger Cooke
This book chronicles the 1936 attack on mathematician
Nikolai Nikolaevich Luzin during the
USSR campaign to “Sovietize” all sciences.
History of Mathematics, Volume 43; 2016; 416 pages;
Hardcover; ISBN: 978-1-4704-2608-8; List US$59; AMS
members US$47.20; Order code HMATH/43
ALGEBRAIC
INEQUALITIES:
NEW VISTAS
Titu Andreescu, The
University of Texas at
Dallas, Richardson, TX
and Mark Saul, Executive
Director, Julia Robinson
Math Festivals
Building both intuitions and formal knowledge
along the way, this book leverages topics in the
traditional high school curriculum to make more
sophisticated results accessible to the reader.
Titles in this series are co-published with the Mathematical Sciences
Research Institute (MSRI).
MSRI Mathematical Circles Library, Volume 19; 2016;
124 pages; Softcover; ISBN: 978-1-4704-3464-9; List
US$41; AMS members US$32.80; Order code MCL/19
GAME THEORY
A PLAYFUL
INTRODUCTION
Matt DeVos, Simon Fraser
University, Burnaby, BC,
Canada and Deborah A.
Kent, Drake University,
Des Moines, IA
Designed as a textbook for
an undergraduate mathematics class, this book
offers a dynamic and rich tour of the mathematics
of both sides of game theory, combinatorial
and classical, and includes generous sets of
exercises at various levels.
Student Mathematical Library, Volume 80; 2016; 343
pages; Softcover; ISBN: 978-1-4704-2210-3; List US$49;
All individuals US$39.20; Order code STML/80
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