Speaker: Andrey Soldatenkov
Date: 10:30 07/04/2023
Title:  Absolute Hodge classes and the Mumford-Tate conjecture for hyperkähler manifolds

Abstract: The Hodge conjecture implies that all Hodge cycles
on a smooth complex projective variety are absolute,
i.e. they remain Hodge if one conjugates the variety by an
automorphism of the field of complex numbers. It was shown
by Deligne that all Hodge cycles on abelian varieties
are absolute, although the Hodge conjecture for abelian
varieties remains open. I will present my recent results
about Hodge cycles on compact hyperkähler manifolds, showing
that all Hodge cycles on all known examples of such manifolds
are absolute. I will also discuss the related results on the
Mumford-Tate conjecture for hyperkähler manifolds.