3. Postdoctoral Program - MSRI

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⎛ ⎜ 1 ⎜ 0 ⎜ 0 ⎜ 0 ⎜ 0 ⎜ 0 ⎜ 0 ⎜ 0 ⎜ 0 ⎜ ⎝ 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 g(m12)+g(m13)−g(m23 2 g(m12)−g(m13)+g(m23 2 −g(m12)+g(m13)+g(m23) 2 −g(m12)−g(m13)+g(m23)+2g(m14) 2 −g(m12)−g(m13)+g(m23)+2g(m15) 2 g(m13) − g(m14) − g(m23) + g(m24) g(m13) − g(m15) − g(m23) + g(m25) g(m12) − g(m14) − g(m23) + g(m34) g(m12) − g(m15) − g(m23) + g(m35) ⎟ ⎠ 0 0 0 0 0 g(m12) + g(m13) − g(m14) − g(m15) − g(m23) + g(m45) From this matrix, we get the equations: x1 = g(m12) + g(m13) − g(m23) 2 x2 = g(m12) − g(m13) + g(m23) 2 x3 = −g(m12) + g(m13) + g(m23) 2 x4 = −g(m12) − g(m13) + g(m23) + 2g(m14) 2 x5 = −g(m12) − g(m13) + g(m23) + 2g(m15) 2 12 ⎞
Figure 3: The hyperbola 2xy + x + y + 2 = 0 2.7 Rational Distance Sets on the Hyperbola Theorem 6. Let a, b, c, d ∈ Q such that ad − bc �= 0, then there exists a rational distance set of three rational points, S = {P1, P2, P3} on the hyperbola axy + bx + cy + d = 0. Proof. The proof will proceed in several parts. First, we rewrite the distance formula as in equation 1. So, yi−yj xi−xj can be paramterized like yi−yj xi−xj = m2 ij −1 2mij . Now, we can solve for yi in our equation for the hyperbola to get the expression: yi = − bxi+d axi+c . We then substitute yi into our modified distance formula and this gives the equation ad−bc (axi+c)(axj+c) = yi−yj xi−xj = m2 ij −1 2mij . Let D = ad − bc. If we take m2 −1 2m = Dn2 and make the substitutions m = X 2D and n = Y 2DX we get the elliptic curve E (D) : Y 2 = X 3 − 4D 2 X. We can also obtain the expression m2 −1 2m = Dn2 from E (D) with the substitutions X = 2Dm and Y = 4D 2 mn. Now, if we let Qi = (Xi: Yi: 1) be rational points on E (D) , then we define the 13
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Final Report, 2005-2010 and Annual
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6. Appendix - Final Reports .......
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• Spring 2008: Representation The
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place the highest value on the oppo
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which establishes the relation betw
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Public Understanding of Mathematics
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1.3 Scientific Programs and their A
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The first week of May 2010 coincide
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The goal of this program was, throu
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"An illustration of the tropical Ab
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• lead to new breakthroughs in th
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Other mathematical breakthroughs th
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• Advice on preparing for intervi
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An off-site workshop partially fund
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1.7 Other Scientific Workshops Hot
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experienced circle leaders. Togethe
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2. Program and Workshop Data 2.1 Pr
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Jöricke Burglind Institut des Haut
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Smith Ivan Centre for Mathematical
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Home Institution Classified by Stat
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2.4 Workshop Participant List (See
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2.7 Program Publication List Last N
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Ghiggini Paolo Sutures and contact
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Lekili Yanki Geometric composition
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Draisma Jan The tropical projective
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Krasner Daniel Patterns in sl(2)-li
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Sarkar Sucharit Murasugi sums Matt
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Falk Michael Feichtner Eva Tropical
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Manolescu Ciprian Manolescu Ciprian
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Steingrimsson Einar Steingrimsson E
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Here are additional details on the
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Kutluhan, Cagatay Lekili, Yanki Cag
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Savelyev, Yakov Vertesi, Vera Yakov
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Katz, Eric Lopez de Medrano, Lucia
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Grigsby, Elisenda Kutluhan, Cagatay
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Sazdanovic, Radmila Wehrli, Stephan
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Angeltveit, Vigleik Crofts, Scott H
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3.2 Postdoctoral Fellow Placement L
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3.4 Postdoctoral Fellow Demographic
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Home Institution Classified by Coun
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SGS 1: IAS/PCMI Summer Workshop: Th
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Jafarov, Elchin University of Alask
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Xie, Yu Purdue University Graduate
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4.3 Program Associates Program Asso
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P r o g r a m A s s o c i a t e s D
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Home Institution Classified by Coun
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5. Undergraduate Program (MSRI-UP)
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This project seeks to use elliptic
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6. Appendix - Final Reports 97
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2 2. Participants The response to o
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4 • Gleb Koshevoy: Bases of tropi
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6 While at MSRI, Gathmann extended
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8 In conclusion, my postdoc at MSRI
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10 -with Christian Haase, who staye
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12 “I was working on the relation
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14 Josephine Yu PhD: UC Berkeley, 2
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16 6. Alex Fink was an invited spea
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Tropical Geometry Postdoctoral Fell
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Tropical Geometry Demographic Summa
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Ozsváth-Szabó Heegaard homology t
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field. Nevertheless, some of it is
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developments which occurred in this
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the audience would know a little ab
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on the group of Hamiltonian diffeom
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German Research Foundation Mentor:
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Mark spend his time at MSRI working
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PhD: University of Texas, 2007 Posi
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example Gadbled, Mandini, Ma’u, H
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Symplectic and Contact Geometry and
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Symplectic and Contact Geometry and
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2 REPORT ON THE MSRI WORKSHOP “HO
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Homology Theory of Knots and Links
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Complementary Program August 17, 20
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Complementary Program 2009-10 Postd
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Complementary Program Demographic S
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MID YEAR REPORT - DECEMBER 2009 VIG
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California. We talked about several
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EXTERNAL POSTDOCTORAL FELLOW REPORT
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on. While his research area is some
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POSTDOCTORAL FELLOW REPORT December
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[1] (with Garcia-Puente, Martin del
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REPORT FROM MENTOR June 2010 Year e
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I have also begun working on relate
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2 Professional Travel Sep. 6 - 26,
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REPORT FROM MENTOR June 2010 Karl h
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POSTDOCTORAL FELLOW REPORT June 201
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REPORT FROM MENTOR June 2010 ------
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Postdoctoral Program supported by t
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RO(S 1 )-graded homotopy groups of
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MSRI POSTDOCTORAL FELLOWSHIP REPORT
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2 TRISTRAM BOGART and its facets ar
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To Whom It May Concern: During the
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MSRI FELLOWSHIP FINAL REPORT SCOTT
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As his mentor at UCSC, I had freque
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- UC Davis Combinatorics Seminar -
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Christopher J. Hillar University of
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G. Isely, C. Hillar, and F. Sommer,
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Postdoc Report for: Dr. Christopher
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2 NSF REPORT FOR ERIC KATZ linear s
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Year-End Report 2010-11 NSF Math In
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Jan. 25 - 28, 2011 Recruitment Visi
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MSRI POSTDOCTORAL FELLOWSHIP REPORT
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Final report: mentoring Sikimeti Ma
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eginning of the Fall semester, and
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MSRI FINAL REPORT JARED SPECK 1. Ba
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External Postdoctoral Fellows 2009-
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External Postdoctoral Fellows 2009-
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2 connections to geometry, topology
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Connections for Women: Tropical Geo
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Participant List MSRI Workshop: Con
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Connections for Women: Tropical Geo
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2 Combinatorics, Several Complex Va
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Introductory Workshop: Tropical Geo
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Currently Available Videos � Sam
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Name Institution Hering, Milena Uni
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Introductory Workshop: Tropical Geo
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analysis. The clarity of Payne’s
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Tropical Geometry in Combinatorics
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Name Institution Kharlamov, Viatche
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Tropical Geometry in Combinatorics
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Above satisfactory 35 73% Somewhat
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Tropical structures in geometry and
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Research Workshop: Tropical Structu
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Research Workshop: Tropical Structu
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Algebraic Structures in the Theory
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2 WORKSHOP REPORT toric fibrations,
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Algebraic Structures in the Theory
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Wednesday November 18, 2009 09:00AM
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Participant List MSRI Workshop: Alg
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Name Institution Smith, Ivan Centre
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Research Workshop: Symplectic and C
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Detailed review: We will now discus
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Symplectic and Contact Topology and
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Research Workshop: Symplectic and C
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Final Report MSRI Connections for W
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Connections : Symplectic and Contac
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Currently Available Videos � Siki
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Milin, Isidora University of Illino
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Final Report Introductory Workshop
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at a variety of levels. Since a hig
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Introductory Workshop: Symplectic a
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Participant List MSRI Workshop: Int
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Park, Jongil Seoul National Univers
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Symplectic and Poisson Geometry in
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Symplectic and Poisson Geometry in
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Symplectic Geometry, Noncommutative
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09:00AM - 10:00AM Registration 10:0
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REPORT ON THE MSRI WORKSHOP “HOMO
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of the theory via webs and foams mo
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Schedule Connections for Women: Hom
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Connections for Women: Homology The
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04/29/2010 Connections for Women: H
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REPORT ON THE MSRI WORKSHOP “INTR
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INTRODUCTORY WORKSHOP, FINAL REPORT
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Introductory Workshop: Homology The
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Connections for Women: Homology The
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Research Workshop: Homology Theorie
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Schedule Research Workshop: Homolog
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Currently Available Videos Research
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Research Workshop: Homology Theorie
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04/29/2010 Research Workshop: Homol
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comprehensive lectures explaining t
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Hot Topics: Black Holes in Relativi
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Currently Available Videos � Miha
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Shao, Shuanglin Institute for Advan
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MATHEMATICAL SCIENCES RESEARCH INST
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MPDI Summer Institute 2009: Final R
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school teachers (in the case of sim
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in length)? The audience would be e
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Evaluation #1 1. What were the bene
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6. Do you have to report to an admi
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your class because your way of teac
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employee with a summary of what you
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what have you learned in this insti
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Evaluation #9 (signed Kelly L.) 1.
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therefore should not be given the j
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would you like them organized? Plea
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Evaluation #11 1. What were the ben
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Evaluation #12 (signed Jake Disston
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ideas are insignificant in light of
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manipulative and pictorial level. F
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Yes.. I would like to talk to 4 - 6
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No, but I have continued to make my
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