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DTSTART:20180325T030000
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DTSTAMP:20191023T163952Z
UID:59cb91e567fc3976690492@ist.ac.at
DTSTART:20181018T133000
DTEND:20181018T153000
DESCRIPTION:Speaker: Nikita Nikolaev\nhosted by Tamas Hausel\nAbstract: I w
ill describe an approach to studying meromorphic connections on vector bun
dles called abelianisation. This technique has its origins in the works of
Fock-Goncharov (2006) and Gaiotto-Moore-Neitzke (2013)\, as well as the W
KB analysis. Its essence is to put rank-n connections on a complex curve X
in correspondence with much simpler objects: connections on line bundles
over an n-fold cover Σ -> X. The point of view is similar in spirit to
abelianisation of Higgs bundles\, aka the spectral correspondence: Higgs
bundles on X are put in correspondence with rank-one Higgs line bundles on
a spectral cover Σ -> X. However\, unlike Higgs bundles\, abelianisat
ion of connections requires the introduction of a new object\, which we ca
ll the Voros cocycle. The Voros cocycle is a cohomological way to encode o
bjects such as ideal triangulations that appeared in Fock-Goncharov\, spec
tral networks that appeared in Gaiotto-Moore-Neitzke\, as well as the conn
ection matrices appearing in the WKB analysis. By focusing our attention o
n the simplest case of logarithmic singularities with generic residues\, I
will describe an equivalence of categories\, which I call the abelianisat
ion functor\, between sl(2)-connections on X satisfying a certain transver
sality condition and rank-one connections on an appropriate 2-fold spectra
l cover Σ -> X. This presentation is based on the work completed in
my thesis (2018) and recent extensions thereof.
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
T Austria
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Abelianisation of Logarithmic sl(2)-Connections
URL:https://talks-calendar.app.ist.ac.at/events/1378
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