3. Postdoctoral Program - MSRI

MSRI POSTDOCTORAL FELLOWSHIP REPORT FOR
VIGLEIK ANGELTVEIT
J. PETER MAY
Vigleik has been a mainstay of the program in algebraic topology at the University
of Chicago for the past five years. He has been the main organizer and a
key participant in our seminars, both those with internal and those with external
speakers. He has been hugely helpful in helping me mentor graduate students. Nine
students of mine obtained their PhD’s in the five years since his arrival, three of
them winning NSF postdoctoral fellowships. Vigleik has been a positive influence
on all of them and on five other graduate students still working with me. For example,
he has given masterly introductions to spectral sequences which have really
taught my students how to use them.
Vigleik is a master of deep calculation and conceptual understanding. His calculations
in and around algebraic K-theory, T HH (Topological Hochschild Homology)
and T C (Topological Cyclic homology) are quite incredibly difficult and very
illuminating. I am especially impressed with his recent work with Teena Gerhardt
which uses calculations of RO(G)-graded homotopy groups to obtain information
about the non-equivariant algebraic K-theory of certain rings. I am also very impressed
by the progress he has made on computing the algebraic K-theory of the
rings Z/p n . When n = 1, this is of course given by Quillen’s calculations of the
K-theory of finite fields, around 30 years ago. For n ≥ 2, little or no progress was
made in all the time since then, until Vigleik’s impressive new work.
I am very grateful that his fellowship has made it possible for him to stay in
Chicago the past two years. His presence has been invaluable.
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