What is the Affine Grassmanian?

Abstract: Affine Grassmannians are infinite-dimensional spaces which play an important role in geometric representation theory. One part of the richness of these spaces is that they can defined in several seemingly distinct ways: via loop groups, via a moduli space of principal bundles, via Kac-Moody groups, or via lattices. In this talk we'll overview the definition of the affine Grassmannian, with some motivation from number theory, and discuss a few examples which relate back to (possibly) more familiar spaces like the nilpotent cone. Finally, if time permits, we'll touch on more advanced topics such as the geometric Satake equivalence.

algebraic geometrycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: learners

What is ...? Seminar

Series comments: The ``What is ... ? Seminar'' (WiSe) is a weekly Zoom mathematics seminar. The goal is to explain interesting things to each other in a casual manner. The name is inspired by the What is ...? column of the Notices of the American Mathematical Society. See the website for more details. If you want to receive the zoom link for the talks please fill out the form linked on the website or contact Anna at a.puskas@uq.edu.au.