Speaker: Jack Davies – University of Bonn
Abstract: Topological $K$-theory has a natural extension to a $G$-equivariant cohomology theory for compact Lie groups $G$—one just simply exchanges vector bundles with $G$-equivariant vector bundles in the usual construction of $K$-theory. There is a reinterpretation of this equivariant cohomology theory though, in terms of algebraic geometry. Although this second perspective could be taken as an insightful curiosity for $K$-theory, for equivariant elliptic cohomology this perspective becomes our (only) definition. In this talk, we will discuss this motivation from $K$-theory in more detail, how it naturally leads one to equivariant elliptic cohomology, and also some other recent results in the field.