Topology Seminar
Past Talks
Fall 2018

 Oct 162018
Inna Zakharevich (Cornell University)
Deriving motivic measures
A motivic measure with values in an abelian group A is a function μ: {varieties}→ A which is additive, in the sense that for any closed embedding Y\hookrightarrow X we have μ(X) = μ(Y)+μ(X\Y). Many such measures, such as point counting, Euler characteristics, or the local zeta function actually take values in a K_{0}group. In this talk we will give a description of how to lift such measures to maps between spectra and show how to use these to find nontrivi elements in higher Kgroups of varieties.
Pretalk abstract: I will give a short introduction to algebraic Ktheory, focusing mostly on exact categories and the Qconstruction.

 Oct 092018
Dan BerwickEvans (UIUC)
A geometric model for complex analytic equivariant elliptic cohomology
Elliptic cohomology is a natural big brother to ordinary cohomology and Ktheory. In contrast to the geometric objects that provide representatives for cohomology and Ktheory classes (which lead to many applications), as yet there is no such geometric description of elliptic cohomology. This talk will explain a step forward, in joint work with Arnav Tripathy, for the case of equivariant elliptic cohomology over the complex numbers. The geometric objects of interest are inspired by supersymmetric gauge theory. No prior knowledge of either elliptic cohomology or gauge theories will be assumed.