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SUMMARY:Non-commutative methods in deformation theory of Hilbert schemes o
 f points on surfaces. - Lie Fu (University of Strasbourg)
DTSTART:20240507T090000Z
DTEND:20240507T100000Z
UID:TALK216703@talks.cam.ac.uk
DESCRIPTION:Abstract: We study the deformation theory of Hilbert schemes o
 f points on surfaces by looking more broadly at the deformation theory of 
 their derived categories\, which is controlled by the Hochschild cohomolog
 y. In this way\, we recover\, unify\, and extend the previous works of Fan
 techi\, Hitchin\, and Boissi&egrave\;re. One interesting finding is that t
 he Hochschild cohomology of a Hilbert scheme of a surface not only depends
  on that of the surface\, but also on the more generally bigraded cohomolo
 gy theory called Hochschild-Serre cohomology of the surface. Our method co
 mputes the Hochschild-Serre cohomology of the symmetric stack [X^n/S_n] in
  terms of the Hochschild-Serre cohomology of X.\nThis is based on a joint 
 work with Pieter Belmans and Andreas Krug\, arXiv:2309.06244.
LOCATION:Seminar Room 1\, Newton Institute
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