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DTSTART:20180325T030000
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DTSTAMP:20260406T173339Z
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
 TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Nikita Nikolaev: Abelianisation of Logarithmic sl(2)-Connections
URL:https://talks-calendar.ista.ac.at/events/1378
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