## Algebraic Geometry Seminar

Philip Engel

UIC

Local systems underlying variation of Hodge structure

**Abstract:**Deligne proved in 1987 that only finitely many Z-local systems of a fixed rank underlie a polarized variation of Hodge structure, over a fixed quasiprojective variety. He conjectured that this finiteness also holds in families of quasiprojective varieties. In the 1990’s, Simpson’s refined this conjecture in the following form: the nonabelian Hodge locus is algebraic. I will discuss joint work with Salim Tayou proving these conjectures when the algebraic monodromy group is cocompact.

Monday September 9, 2024 at 3:00 PM in 636 SEO