Seminars Calendar

Monday December 5, 2022 - 15:00 - via Zoom - Simon Pepin Lehalleur (Radboud University, Nimega)

Motivic mirror symmetry for Higgs bundles

Abstract: The moduli spaces of semistable Higgs bundles over a smooth projective curve for two Langlands dual groups are conjecturally related by a form of mirror symmetry, the semi-classical limit of the Geometric Langlands correspondence. In the case of \(SL_n\) and \(PGL_n\), Hausel and Thaddeus conjectured that this mirror symmetry should be reflected in a specific identity of (twisted orbifold) Hodge numbers, which was then proven by Groechenig, Wyss and Ziegler. I will explain that this identity lifts to an isomorphism of (Voevodsky) motives with rational coefficients. The method is based on another proof of the Hausel-Thaddeus conjecture due to Maulik and Shen, combined with extensions of our previous result that motives of moduli of \(GL_n\)-Higgs bundles are direct summands of motives of abelian varieties. I will start with a brief introduction to motives and to moduli spaces of bundles on curves. Joint work with Victoria Hoskins (Nijmegen).

Working Seminars

Condensed mathematics 2022

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