Chern classes, perverse filtrations, and Fourier transforms

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• Junliang Shen (Yale University)
• Monday 17 June 2024, 15:30-16:30
• Seminar Room 1, Newton Institute.

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EMGW05 - Moduli stacks and enumerative geometry

Chern classes of universal families have played a crucial role in the study of cohomology of the moduli of stable vector bundles on Riemann surfaces since the work of Mumford and Atiyah-Bott over 40 years ago. In recent years, the study of cohomological aspects of non-abelian Hodge theory (the P=W conjecture) and enumerative geometry (Gopakumar-Vafa theory) links Chern classes to a very different structure—- the perverse filtration for certain moduli of sheaves and Higgs bundles. I will first review this phenomenon. Then I will discuss a theory of Fourier transform which explains this link. Based on joint work with Davesh Maulik and Qizheng Yin.

This talk is part of the Isaac Newton Institute Seminar Series series.

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