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SUMMARY:Oscar Garcia-Prada (ICMAT\, Spain)
DTSTART:20210325T130000Z
DTEND:20210325T150000Z
DTSTAMP:20260423T005758Z
UID:AGNTISTA/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGNTISTA/31/
 ">Arakelov–Milnor inequalities and maximal variations of Hodge structure
 </a>\nby Oscar Garcia-Prada (ICMAT\, Spain) as part of Algebraic Geometry 
 and Number Theory seminar - ISTA\n\n\nAbstract\nIn this talk we study the 
 fixed points under the action of the multiplicative group of non-vanishing
  complex numbers on moduli spaces of Higgs bundles over a compact Riemann 
 surface for complex semisimple Lie groups and their real forms. These fixe
 d points are called Hodge bundles and correspond to complex variations of 
 Hodge structure. We introduce a topological invariant for Hodge bundles th
 at generalizes the Toledo invariant appearing for Hermitian Lie groups. A 
 main result to discuss is a bound on this invariant which generalizes both
  the Milnor–Wood inequality of the Hermitian case\, and the Arakelov ine
 qualities of classical variations of Hodge structure. When the generalized
  Toledo invariant is maximal\, we establish rigidity results for the assoc
 iated variations of Hodge structure which generalize known rigidity result
 s for maximal Higgs bundles and their associated maximal representations i
 n the Hermitian case (based on joint work with Olivier Biquard\, Brian Col
 lier and Domingo Toledo).\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/31/
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