## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** Gauge theory and homotopical representation theory

**Speaker:** Dan Ramras

**Speaker Info:** Vanderbilt

**Brief Description:**

**Special Note**:

**Abstract:**

The deformation K-theory spectrum of a discrete group G, introduced by Gunnar Carlsson, can be thought of as a homotopy theoretical analogue of the representation ring. Computations suggest that for many infinite discrete groups G with compact classifying spaces, deformation K-theory will agree with topological K-theory of BG (but only above the rational cohomological dimension of G minus 2). The relationship with K-theory is reminiscent of the Atiyah-Segal theorem, while the failure in low dimensions is precisely analogous to the low dimensional failure in the Quillen-Lichtenbaum conjecture (which relates algebraic K-theory to etale K-theory). When BG = M is a manifold, the relationship between deformation K-theory and topological K-theory can be interpreted in terms of gauge theory on principal bundles over M.
This perspective, together with work of Tyler Lawson, has been used to calculate deformation K-theory for products of (possibly non-orientable) surfaces. I'll explain these results and, time permitting, ongoing joint work with Tom Baird which explicitly produces the low-dimensional failure in many cases.

**Date:** Monday, October 20, 2008

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Prof. Paul Goerss

**Contact email:** pgoerss@math.northwestern.edu

**Contact Phone:** 847-491-8544

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