EVENT DETAILS AND ABSTRACT

Title: Topology of the Affine Springer Fibers: examples and applications to the representation theory
Speaker: Alexei Oblomkov
Speaker Info: University of Massachusetts Amherst
Brief Description:
Special Note:
Abstract:

The talk is based on joint work with Zhiwei Yun. Given an element $a\in \mathfrak{g}[[t]]$, the affine Springer is the locus inside affine Grassmanian of type $\mathfrak{g}$ fixed by $a$. In my talk I explain the construction of the action of the rational Cherednik algebra on the cohomology of the affine Springer fibers that admit $\mathbb{C}^*$-action. To demonstrate the richness of the subject I will discuss in details the Affine Springer Fibers for the algebras $\mathfrak{g}$ of rank $2$: many familiar objects like elliptic curves and $K3$-surfaces will appear as examples of $\CC^*$-fixed locus of such Springer fibers. If time permits, I would also discuss a conjectural relation between the Affine Springer fibers and knot invariants.