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SUMMARY:Robert Hanson (IST Lisbon)
DTSTART:20220527T160000Z
DTEND:20220527T170000Z
DTSTAMP:20260404T094121Z
UID:GeometricStrNxtGn/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Geome
 tricStrNxtGn/1/">Fourier-Mukai Transforms for Compactified Prym Varieties<
 /a>\nby Robert Hanson (IST Lisbon) as part of Geometric Structures - NextG
 en\n\n\nAbstract\nModuli of Higgs bundles naturally fit into an SYZ mirror
  symmetry picture\, which predicts dualities on the fibers of the Hitchin 
 fibration. We shall explore these predictions for the structure groups G =
  GL_n and G = SL_n\, connecting work of Dima Arinkin with a forthcoming pa
 per of Emilio Franco\, João Ruano and myself.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricStrNxtGn/1/
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BEGIN:VEVENT
SUMMARY:Karim Rega (University of Edinburgh)
DTSTART:20220627T160000Z
DTEND:20220627T170000Z
DTSTAMP:20260404T094121Z
UID:GeometricStrNxtGn/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Geome
 tricStrNxtGn/2/">Parahoric Higgs Sheaves</a>\nby Karim Rega (University of
  Edinburgh) as part of Geometric Structures - NextGen\n\n\nAbstract\nSoon 
 after the development of the theory of Higgs bundles and non-abelian Hodge
  theory on complex projective curves\, Simpson looked at the formulation o
 f these notions over punctured curves.  Earlier work for regular bundles b
 y Mehta and Seshadri already showed that the natural structure here is tha
 t of a parabolic bundle\, leading to the notion of a parabolic Higgs bundl
 e. Recently\, it has become clear that a more uniform way to look at these
  subjects is through the study of parahoric torsors. In this talk I will a
 ttempt to motivate the need for the parahoric story\, give some elements o
 f the definition and formulate the notion of a parahoric Higgs bundle\n
LOCATION:https://stable.researchseminars.org/talk/GeometricStrNxtGn/2/
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BEGIN:VEVENT
SUMMARY:Alex Nolte (Rice University)
DTSTART:20220923T160000Z
DTEND:20220923T170000Z
DTSTAMP:20260404T094121Z
UID:GeometricStrNxtGn/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Geome
 tricStrNxtGn/3/">Higher Complex Structures and SL(3\,R) Hitchin Components
 </a>\nby Alex Nolte (Rice University) as part of Geometric Structures - Ne
 xtGen\n\n\nAbstract\nA source of richness in Teichmüller theory is that T
 eichmüller spaces have descriptions both in terms of group representation
 s and in terms of hyperbolic and complex structures. A program in higher-r
 ank Teichmüller theory is to understand to what extent there are analogou
 s geometric interpretations of Hitchin components. In this talk\, I'll dis
 cuss higher degree complex structures\, which were defined by Fock and Tho
 mas and are conjectured to parameterize SL(n\,R) Hitchin components. I'll 
 then talk about recent results describing the SL(3\,R) Hitchin component i
 n terms of higher complex structures\, and some intrinsic structural featu
 res of Fock-Thomas spaces.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricStrNxtGn/3/
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