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Junliang Shen (Yale University)
Monday 17 June 2024, 15:30-16:30
Chern classes, perverse filtrations, and Fourier transforms
- đ¤ Speaker: Junliang Shen (Yale University)
- đ Date & Time: Monday 17 June 2024, 15:30 - 16:30
- đ Venue: Seminar Room 1, Newton Institute
Abstract
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.
Series This talk is part of the Isaac Newton Institute Seminar Series series.
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