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BIMSA AG Seminar
BIMSA AG Seminar
Motivic classes of Higgs bundles and of bundles with connections
Motivic classes of Higgs bundles and of bundles with connections
Organizers
Speaker
Roman Fedorov
Time
Thursday, March 20, 2025 10:00 AM - 11:00 AM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
Let $X$ be a smooth geometrically connected projective curve over a field $k$. Consider the moduli stacks $Higgs_{r,d}(X)$ of rank $r$ degree d Higgs bundles on $X$. When $k$ is a finite field, O. Schiffmann and S. Mozgovoy calculated the volumes of the semistable parts of these stacks. Their formulas were significantly simplified by A. Mellit.
In a joint work with A. Soibelman and Y. Soibelman, the speaker has calculated the motivic volume of the above stacks when k has characteristic zero. We also calculated the motivic volumes of the stacks $Conn_r(X)$ of rank $r$ vector bundles with connections. We extended these results to the case of Higgs bundles with connections with singularities (including generic irregular singularities). I will discuss these results and give a brief overview of the strategies of
the proofs.
In a joint work with A. Soibelman and Y. Soibelman, the speaker has calculated the motivic volume of the above stacks when k has characteristic zero. We also calculated the motivic volumes of the stacks $Conn_r(X)$ of rank $r$ vector bundles with connections. We extended these results to the case of Higgs bundles with connections with singularities (including generic irregular singularities). I will discuss these results and give a brief overview of the strategies of
the proofs.