3. Postdoctoral Program - MSRI

MSRI POSTDOCTORAL FELLOWSHIP FINAL REPORT
VIGLEIK ANGELTVEIT
Abstract. This is the final report for my MSRI postdoctoral fellowship, August
2010 to May 2011. Section 1 contains some biographical data I have been
asked to supply. Section 2 contains a summary of my research while being a
postdoctoral fellow.
1. Biography
Name: Vigleik Angeltveit
Year of Ph.D: 2006
Institution of Ph.D.: Massachusetts Institute of Technology
Ph.D. advisor: Haynes Miller
Institution prior to obtaining the MSRI PD fellowship: University of Chicago
Position at that institution: Dickson Instructor (postdoc)
Mentor (if applicable): J. Peter May
Institution where you held your MSRI PD fellowship: University of Chicago
Mentor at that institution: J. Peter May
Institution (or company) where you are going next year: Australian National University
Position: Lecturer, academic level B. (Permanent position, approximately equivalent
to tenure track assistant professorship.)
Anticipated lenght: Permanent
2. Research in the last two years
As a postdoctoral fellow I finished two papers that were started before the fellowship,
I finished at least one paper that was started during the fellowship, and I
have started several new projects that are still ongoing.
2.1. Algebraic K-theory computations using RO(S 1 )-graded homotopy
groups. This is a multi-paper project joint with Teena Gerhardt and/or Lars
Hesselholt. The basic idea is that a sufficiently good understanding of topological
Hochschild homology (T HH) of a ring or ring spectrum leads to calculations in
algebraic K-theory. While such calculations are extremely difficult it is worth the
effort because algebraic K-theory lies in the intersection of fields such as algebraic
number theory, algebraic geometry and geometric topology.
The topological Hochshild homology spectrum T HH(A) is a genuine S 1 -spectrum
in the sense that it is indexed on S 1 -representations rather than integers.
As such it, and its fixed points, have homotopy groups indexed on the real representation
ring RO(S 1 ) rather than the integers. While the calculation of K(A)
ultimately only depends on the integer-graded homotopy groups of T HH(A), the
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