Abstract: 

A.Grothendieck conjectured that a vector bundle with connection on a curve over a number field has all flat sections in algebraic functions iff 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. 

Speaker:

Maxim KONTSEVICH, Permanent professor at Institut des Hautes Études Scientifiques.

Awards:   

- Otto Hahn Medal, Max-Planck-Gesellschaft, 1992

- Prix de la Mairie de Paris, Premier Congrès Européen de Mathématiques, 1992

- Henri Poincaré Prize, 1997

- Prize of the International Congress of Mathematical Physics, Brisbane, 1997

- Fields Medal, IMU, ICM Berlin, 1998

- Crafoord Prize, 2008

- Shaw Prize in Mathematical Sciences, 2012

- Fundamental Physics Prize, 2012

- Breakthrough Prize in Mathematics, 2014

Video：http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=On_Grothendieck_s_Algebraicity_Conjecture_and_random_matrices.html