Geometry & Topology Seminar

Upcoming Seminars

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.

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.

Aji Dhillon
Nov 14, 15:30 - 16:30
MC 107