EVENT DETAILS AND ABSTRACT

Title: Equivariant (K-)homology of affine Grassmannian and Toda lattice
Speaker: Professor Michael Finkelberg
Speaker Info: Independent Moscow University
Brief Description:
Special Note:
Abstract:

Let G be a semi-simple compact Lie group with complexification G_c; the group \omega G of based polynomial loops into G is also known as the affine Grassmannian Gr_{G_c} of G_c. Certain topological invariants of \omega G are studied in the geometric Langlands duality theory, and are related to the Langlands dual group \check G_c. We describe a new (algebro-geometric) invariant of this kind: the monoidal category of equivariant perverse coherent sheaves on Gr_{G_c}. We compute its Grothendieck ring K^G(Gr_{G_c}), and an 'additive' analogue of the latter, the equivariant homology H^G(\omega G) ('equivariant loop homology of G'). We identify H^G(\omega G) with the completed Kostant Toda lattice for \check G_c. Time permitting, we will discuss conjectures relating these results to a 'quantization' of the Beilinson-Drinfeld geometric Langlands conjecture, and also a classical limit of this conjecture; and relation to Feigin-Loktev fusion product of G_c- modules.