Motivic Classes for Moduli of Connections

          @misc{ pirsa_PIRSA:17020023,
            doi = {10.48660/17020023},
            url = {https://pirsa.org/17020023},
            author = {Soibelman, Alexander},
            keywords = {Mathematical physics},
            language = {en},
            title = {Motivic Classes for Moduli of Connections},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {feb},
            note = {PIRSA:17020023 see, \url{https://pirsa.org}}
          }
          

Abstract

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 a work in progress with Roman Fedorov and Yan Soibelman.