Maxim KONTSEVICH - On Grothendieck's Algebraicity Conjecture and random matrices

YMSC-Tsinghua Modern Mathematics Lecture Series
2023-03-26
Speaker: Maxim KONTSEVICH (IHES), 1998 Fields Medalist
Title:
On Grothendieck's Algebraicity Conjecture and random matrices
Abstract:
A.Grothendieck conjectured that a vector bundle with connection on a curve over a number field has all flat sections in algebraic functions if the p-curvature vanishes for almost all primes p. In 1984 D.Chudnovsky and G.Chudnovsky proved Grothendieck's Algebraicity Conjecture in the abelian case: if the derivative of logarithm of a series with integer coefficients is algebraic, then the series itself is algebraic. I'll talk about the application of this result in the theory of large random unitary matrices, based on theory of algebraic noncommutative series by N.Chomsky and M.Schützenberger.
References:
Slides:
About the speaker:
Professor Kontsevich is one of the leading mathematicians and mathematical physicists of the 20th and 21st centuries with outstanding contributions to algebraic geometry, algebraic topology and geometric aspects of mathematical physics, such as knot theory, quantization and mirror symmetry.
He received the Henri Poincaré Prize in 1997, the FieldsMedal in 1998, the Crafoord Prize in 2008, the Shaw Prizeand Fundamental Physics Prize in 2012, and the Breakthrough Prize in Mathematics in 2014.
Speaker Homepage:
www.ihes.fr/~maxim/
Webpage of the talk:
ymsc.tsinghua.edu.cn/en/info/...
Webpage of the YMSC-Tsinghua Modern Mathematics Lecture Series:
ymsc.tsinghua.edu.cn/en/Activ...

The speaker is presented at 3:36. He starts to speak at 6:10 (better sound).

[@camellkachour4112]

Maxim n'est pas qu'un grand mathématicien, c'est un homme extrêmement simple et d'une grande gentillesse !