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SUMMARY:Junliang Shen (Yale University)
DTSTART:20240126T200000Z
DTEND:20240126T210000Z
DTSTAMP:20260406T162359Z
UID:agstanford/130
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/1
 30/">Geometry of the P=W conjecture and beyond</a>\nby Junliang Shen (Yale
  University) as part of Stanford algebraic geometry seminar\n\nLecture hel
 d in 383-N.\n\nAbstract\nGiven a compact Riemann surface\, nonabelian Hodg
 e theory relates topological and algebro-geometric objects associated to i
 t. Specifically\, complex representations of the fundamental group are in 
 correspondence with algebraic vector bundles\, equipped with an extra stru
 cture called a Higgs field. This gives a transcendental matching between t
 wo very different moduli spaces associated with the Riemann surface: the c
 haracter variety (parameterizing representations of the fundamental group)
  and the Hitchin moduli space (parameterizing Higgs bundles). In 2010\, de
  Cataldo\, Hausel\, and Migliorini proposed the P=W conjecture\, which giv
 es a precise link between the topology of the Hitchin space and the Hodge 
 theory of the character variety\, imposing surprising constraints on each 
 side. I will introduce the conjecture\, review its recent proofs\, and dis
 cuss how the geometry hidden behind the P=W phenomenon is connected to oth
 er branches of mathematics.\n
LOCATION:https://researchseminars.org/talk/agstanford/130/
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