Galois theory of period and the André-Oort conjecture
Hot Topics: Galois Theory of Periods and Applications March 27, 2017 - March 31, 2017
Location: MSRI: Simons Auditorium
Galois theory
Periods
Galois orbits
integration
algebraic varieties
algebraic geometry
motivic geometry
Kontsevich conjecture
transcendental numbers
number fields
de Rham cohomology
abelian varieties
11Rxx - Algebraic number theory: global fields {For complex multiplication, see 11G15}
14C35 - Applications of methods of algebraic $K$-theory [See also 19Exx]
14C30 - Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture
14F42 - Motivic cohomology; motivic homotopy theory [See also 19E15]
Andre
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
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Andre
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