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DESCRIPTION:Speaker: Ben Davison (University of Edinburgh)\n\nAbstract: Th
is is the third of a series of 3 lectures.\n\nThe nonabelian Hodge correspo
ndence provides a diffeomorphism between certain coarse moduli spaces of se
mistable Higgs bundles on a smooth projective curve C (the Dolbeault side)
and coarse moduli spaces of representations of the fundamental group of C (
the Betti side). In the case of coprime rank and degree\, these spaces are
smooth\, and the famous P=W conjecture states that the isomorphism in coho
mology provided by the above diffeomorphism takes the weight filtration on
the Betti side to the perverse filtration on the Dolbeault side. The purpo
se of these talks is to use recent advances in cohomological Donaldson-Thom
as theory to extend this story to moduli stacks.\n\nFor coprime rank and de
gree\, two key features in the study of classical nonabelian Hodge theory a
re the perverse filtration with respect to the Hitchin base\, and the purit
y of the cohomology of the Dolbeault moduli space. I will present an exten
sion of the BBDG decomposition theorem to moduli stacks of objects in 2CY c
ategories\, which enables us to reproduce both of the above features for st
acks in nonabelian Hodge theory.\n\nThese results\, along with cohomologica
l Hall algebras\, allow us to connect the intersection cohomology of coarse
moduli spaces with the Borel-Moore homology of the above stacks\, providin
g the connection between three versions of the P=W conjecture: the original
conjecture for smooth moduli spaces\, the version for intersection cohomol
ogy of singular moduli spaces\, and a new version for stacks.
DTEND:20211028T193000Z
DTSTAMP:20220126T152226Z
DTSTART:20211028T183000Z
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SEQUENCE:0
SUMMARY:M-Seminar: Cohomological DT theory and nonabelian Hodge theory for
stacks III
UID:tag:localist.com\,2008:EventInstance_37910207666188
URL:https://events.k-state.edu/event/m-seminar_cohomological_dt_theory_and_
nonabelian_hodge_theory_for_stacks_iii
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