Differential Geometry Seminar: An application of elliptic cohomology to quantum groups

I will start by reviewing quantum groups (including quantum groups at roots of unity, Yangians, etc) and their representation theory. I will then explain the construction of quantum groups using cohomology theories from topology.

The construction uses the so-called cohomological Hall algebra associated to a quiver and an oriented cohomology theory. In examples, we obtain the Yangian, quantum loop algebra and elliptic quantum group, when the cohomology theories are the cohomology, K-theory, and elliptic cohomology respectively. I will explain the application of elliptic cohomology theory in detail.

School of Computer and Mathematical Sciences