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QGM seminar by Alexander Soibelman (Aarhus University)

Title: Motivic classes for moduli of Higgs bundles and moduli of vector bundles with connections on a curve

2018.09.21 | Jane Jamshidi

Date Wed 26 Sep
Time 14:15 15:15
Location 1531-219 (Aud. D4)


In their paper, ”On the motivic class of the stack of bundles”, Behrend and Dhillon prove a motivic version of the Siegel formula for the number of vector bundles on a curve over a finite field. Later, Mozgovoy and Schiffmann computed the number of points over a finite field for the moduli stack of semistable twisted Higgs bundles. We start by discussing motivic classes for stacks. Then, following the approach of Mozgovoy and Schiffmann, we outline an argument for a motivic version of their formula in the case of semistable Higgs bundles and use it to compute the motivic class of the stack of vector bundles with connections on a curve. Finally, we will comment on a variation of this computation when the Higgs bundles and connections are parabolic. This is joint work with Roman Fedorov and Yan Soibelman.