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SUMMARY:Chern classes\, perverse filtrations\,  and Fourier transforms - J
 unliang Shen (Yale University)
DTSTART:20240617T143000Z
DTEND:20240617T153000Z
UID:TALK217669@talks.cam.ac.uk
DESCRIPTION:Chern classes of universal families have played a crucial role
  in the study of cohomology of the moduli of stable vector bundles on Riem
 ann 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 theor
 y) links Chern classes to a very different structure --- the perverse filt
 ration for certain moduli of sheaves and Higgs bundles. I will first revie
 w this phenomenon. Then I will discuss a theory of Fourier transform which
  explains this link. Based on joint work with Davesh Maulik and Qizheng Yi
 n.
LOCATION:Seminar Room 1\, Newton Institute
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