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Galois theory of period and the André-Oort conjecture

Hot Topics: Galois Theory of Periods and Applications March 27, 2017 - March 31, 2017

March 27, 2017 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Yves Andre (Centre National de la Recherche Scientifique (CNRS))
Location: SLMath: Eisenbud Auditorium
Tags/Keywords

  • Galois theory

  • Periods

  • Galois orbits

  • integration

  • algebraic varieties

  • algebraic geometry

  • motivic geometry

  • Kontsevich conjecture

  • transcendental numbers

  • number fields

  • de Rham cohomology

  • abelian varieties

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Andre
Abstract

The idea of a Galois theory of periods comes from an insight of Grothendieck. I shall briefly outline of this (conjectural) theory, then sketch the path which led me from it to the AO conjecture, as well as some paths backward. Principally polarized abelian varieties of dimension  g  are parametrized by the algebraic variety  A_g, those with prescribed extra "symmetries" by special subvarieties of  A_g, and those with maximal symmetry (complex multiplication) by special points. The AO conjecture characterizes special subvarieties of  A_g  by the density of their special points. It has been proven last year, after two decades of collaborative efforts putting together many different areas
Supplements
28366?type=thumb Andre. Notes 126 KB application/pdf Download
Video/Audio Files

Andre

H.264 Video 1-Andre_b2.mp4 111 MB video/mp4 rtsp://videos.msri.org/Andre/1-Andre_b2.mp4 Download
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