Séminaire de Mathématique

Motivic Classes for Moduli of Connections

by Prof. Alexander SOIBELMAN (University of Southern California)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

In their paper, "On the motivic class of the stack of bundles",  Behrend and Dhillon were able to derive a formula for the class of a stack of vector bundles on a curve in a completion of the K-ring of varieties.  Later, Mozgovoy and Schiffmann performed a similar computation in order to obtain the number of points over a finite field in the moduli space of twisted Higgs bundles.  We will briefly introduce motivic classes.  Then, following Mozgovoy and Schiffmann's argument, we will outline an approach for computing motivic classes for the moduli stack of vector bundles with connections on a curve. This is joint work with Roman Fedorov and Yan Soibelman.