Description
Hodge Locus and differential geometry (Ho-Lo-Diff)
I will survey various applications of algebraic differential geometry and Galois theory of foliations to finiteness results in differential geometry. Specifically, I will discuss the study of totally geodesic submanifolds of ball quotients (joint work with Ullmo) and affine invariant submanifolds of strata of abelian differentials (with Urbanik). I will aim to highlight a unifying theme throughout: atypical intersections.
