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VERSION:2.0
PRODID:-//Memento EPFL//
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SUMMARY:Nonabelian Hodge isomorphism for moduli stacks
DTSTART:20220531T131500
DTEND:20220531T150000
DTSTAMP:20260511T044817Z
UID:54c3a7dcbb879d942277e58b0aeb12d3a9c4a2e29c42bf57ced3bdcc
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ben Davison (The University of Edinburgh)\nIf C is a smooth pr
 ojective complex curve\, then by classical nonabelian Hodge theory there i
 s a diffeomorphism between the coarse moduli space of representations of t
 he fundamental group of C\, and the coarse moduli space of degree zero sem
 istable Higgs bundles on C.  In particular\, the Borel-Moore homology of 
 these two moduli spaces is isomorphic.\n\n\nIn this talk I will construct 
 an isomorphism between the Borel-Moore homologies of the full stack of rep
 resentations of the fundamental group and the full stack of degree zero se
 mistable Higgs bundles.  In the absence of any kind of isomorphism betwee
 n these two stacks\, the isomorphism in BM homology has to take a roundabo
 ut route\, via an isomorphism of the "BPS cohomology" of the two moduli pr
 oblems.  This in turn is provided by the classical nonabelian Hodge theor
 y\, along with a freeness result regarding the BPS Lie algebra on both sid
 es of nonabelian Hodge theory.  This is joint work in progress with Lucie
 n Hennecart and Sebastain Schlegel-Mejia.In the first part of the talk I w
 ill introduce some of the objects mentioned above\, including the BPS Lie 
 algebra\, which plays a leading role in the story.\n\n 
LOCATION:GC A1 416 https://plan.epfl.ch/?room==GC%20A1%20416
STATUS:CONFIRMED
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