On Grothendieck's Algebraicity Conjecture and random matrices
Maxim Kontsevich (IHES) - Host: Fabien Morel
16.05.2024 um 16:30 Uhr
Es spricht
Maxim Kontsevich (IHES)
im Mathematischen Institut, Raum A 027,
über das Thema
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 given by 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 a surprising application of this result in the theory of large random unitary matrices, based on the notion of algebraic noncommutative series introduced by N.Chomsky and M.Schützenberger.