Thomas Krämer
Humboldt Universität, Berlin, Germany

An important task in algebraic geometry and Hodge theory is to control the monodromy of families of subvarieties in a given variety. In their recent work on the Shafarevich conjecture, Lawrence and Sawin have shown that any non-isotrivial family of smooth hypersurfaces in an abelian variety has big monodromy when twisted by a generic local system of rank one. I will explain how to go beyond hypersurfaces: The same big monodromy theorem holds for every family of subvarieties of dimension at most half the dimension of the abelian variety. The proof uses a combination of geometric arguments, representation theory and perverse sheaves; this is joint work with Ariyan Javanpeykar, Christian Lehn and Marco Maculan.