Galois theory of period and the AndréOort conjecture
Hot Topics: Galois Theory of Periods and Applications March 27, 2017  March 31, 2017
Location: SLMath: Eisenbud Auditorium
Galois theory
Periods
Galois orbits
integration
algebraic varieties
algebraic geometry
motivic geometry
Kontsevich conjecture
transcendental numbers
number fields
de Rham cohomology
abelian varieties
11Y16  Numbertheoretic algorithms; complexity [See also 68Q25]
14D10  Arithmetic ground fields (finite, local, global) and families or fibrations
14D24  Geometric Langlands program (algebrogeometric aspects) [See also 22E57]
14F40  de Rham cohomology and algebraic geometry [See also 14C30, 32C35, 32L10]
14G40  Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]
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
Andre. Notes

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