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SUMMARY:The decomposition theorem for stacks of Higgs bundles
DTSTART:20211202T141500
DTEND:20211202T160000
DTSTAMP:20260506T100931Z
UID:96f6f8f25416cc47b9f2f70a55e52c662a595e55350d9d2480c3dc3a
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ben Davison (Edinburgh Hodge Institute)\nThe BBDG decompositio
 n theorem is a fundamental result on the cohomology of smooth varieties\, 
 which are proper over some base L\, implying that the cohomology is filter
 ed by the hypercohomology of perverse sheaves on the base L (I'll recall t
 his part of the theory in the pre-talk).  \n\n \n\nOne of the most stri
 king applications of this theory is to the topology of smooth moduli space
 s of Higgs bundles\, which admit a proper morphism\, given by the Hitchin 
 system.  Smoothness is arranged by fixing the rank and the degree of the 
 Higgs bundles under consideration to be coprime.\n\n \n\nIn the main talk
  I will focus on what happens in the non-coprime case\; the moduli space o
 f Higgs bundles then becomes highly singular and stacky\, so that the deco
 mposition theorem doesn't (seem to) apply to the Hitchin system.  I'll ex
 plain why in fact the decomposition theorem still holds\, and sketch an ap
 plication to the famous P=W conjecture\, connecting the perverse filtratio
 n defined via the decomposition theorem on the Dolbeault/Higgs side with t
 he weight filtration on the Betti side of nonabelian Hodge theory.
LOCATION:MA A1 12 https://plan.epfl.ch/?room==MA%20A1%2012
STATUS:CANCELLED
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