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SUMMARY:Simion Filip (University of Chicago)
DTSTART:20211222T121000Z
DTEND:20211222T133000Z
DTSTAMP:20260423T005732Z
UID:GDS/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GDS/46/">Ano
 sov representations\, Hodge theory\, and Lyapunov exponents</a>\nby Simion
  Filip (University of Chicago) as part of Geometry and Dynamics seminar\n\
 n\nAbstract\nDiscrete subgroups of semisimple Lie groups arise in a variet
 y of contexts\, \nsometimes "in nature" as monodromy groups of families of
  algebraic manifolds\, \nand other times in relation to geometric structur
 es and associated dynamical \nsystems. I will discuss a class of such disc
 rete subgroups that arise from \ncertain variations of Hodge structure and
  lead to Anosov representations\, thus \nrelating algebraic and dynamical 
 situations. Among many consequences of these \nrelations\, I will explain 
 Torelli theorems for certain families of Calabi-Yau \nmanifolds (including
  the mirror quintic)\, uniformization results for domains \nof discontinui
 ty of the associated discrete groups\, and also a proof of a \nconjecture 
 of Eskin\, Kontsevich\, Moller\, and Zorich on Lyapunov exponents. \nThe d
 iscrete groups of interest live inside the real linear symplectic group\, 
 \nand the domains of discontinuity are inside Lagrangian Grassmanians and 
 other \nassociated flag manifolds. The necessary context and background wi
 ll be explained.\n
LOCATION:https://researchseminars.org/talk/GDS/46/
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