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SUMMARY:Structures in p-adic Hodge Theory and Representation Theory\, with
  applications to Number Theory
DTSTART:20260122T093000
DTEND:20260122T103000
DTSTAMP:20260415T183552Z
UID:2a72ba7c6c8a387e8d2b0a88444773f3022954e2af5d3410f7a300a9
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Yujie Xu\, Columbia University\nSeminar in Mathematics\n
 \nAbstract: Complex Hodge Theory is a method for studying the cohomology 
 groups of a smooth manifold using partial differential equations. Develope
 d by Hodge in the 1930s\, it uses methods from complex analysis\, complex 
 geometry\, Riemannian geometry\, differential geometry\, PDE and algebraic
  geometry. A key object in play here is the notion of a Hodge structure. 
 \n\nIn number theory\, similar structures exist. The area of p-adic Hodge 
 Theory can be thought of as "complex Hodge theory adapted to number-theore
 tic applications". Such techniques feature heavily in the Langlands Progra
 m\, which threads through different fields such as representation theory (
 of p-adic reductive groups)\, number theory\, algebraic geometry\, and eve
 n the (algebraic) theory of differential equations. \n\nIn this talk\, I 
 will start with motivations coming from classical number theory questions\
 , and explain how representation theory and p-adic Hodge theory have prove
 n to be powerful tools for attacking such questions. I will discuss my var
 ious results in this framework\, and give a brief preview of some current 
 and future projects. \n 
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517 https://epfl.zo
 om.us/j/69710607778
STATUS:CONFIRMED
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