Computing torus-equivariant K-theory of singular varieties

TL;DR

This paper surveys recent advances in computing the equivariant K-theory of singular varieties with torus actions, highlighting new methods and results in the field.

Contribution

It presents a synthesis of recent work on torus-equivariant K-theory of singular varieties, including new computational techniques and theoretical insights.

Findings

Development of methods for computing equivariant K-theory

Application to singular varieties with torus actions

Clarification of the structure of equivariant K-theory in this context

Abstract

This expository note surveys some results on equivariant K-theory of varieties with a torus action, focusing on recent work with Sam Payne and Richard Gonzales. It is based on my contribution to the Clifford Lectures at Tulane University in March 2015.