Oct

03

Karol Szumilo

Oct 03, 15:30 - 16:30

MC 107

Cofibration Categories and Groupoid $C^*$-algebras

I will present a theorem saying that homotopical functors out of a
cofibration category are essentially determined by its subcategory of
cofibrations. As an application I will discuss a functorial
construction of groupoid $C^*$-algebras which is related to the
Baum-Connes Conjecture. This is joint work with Markus Land and
Thomas Nikolaus.

Oct

17

David Anderson

Oct 17, 13:30 - 14:30

MC 107

Operational equivariant $K$-theory

Given any covariant homology theory on algebraic varieties, the bivariant machinery of Fulton and MacPherson constructs an "operational" bivariant theory, which formally includes a contravariant cohomology component. Taking the homology theory to be Chow homology, this is how the Chow cohomology of singular varieties is defined. I will describe joint work with Richard Gonzales and Sam Payne, in which we study the operational $K$-theory associated to the $K$-homology of $T$-equivariant coherent sheaves. Remarkably, despite its very abstract definition, the operational theory has many properties which make it easier to understand than the $K$-theory of vector bundles or perfect complexes. This is illustrated most vividly by singular toric varieties, where relatively little is known about $K$-theory of vector bundles, while the operational equivariant $K$-theory has a simple description in terms of the fan, directly generalizing the smooth case.

Nov

14

Aji Dhillon

Nov 14, 15:30 - 16:30

MC 107

TBA