Oct

16

2024

When:
Wednesday, October 16, 2024

3:00 PM - 4:00 PM CT

Where: Lunt Hall, 107, 2033 Sheridan Road, Evanston, IL 60208 map it

Audience: Faculty/Staff - Student - Public - Post Docs/Docs - Graduate Students

Contact:
Yuchen Liu
(847) 491-5553

Group: Department of Mathematics: Algebraic Geometry Seminar

Category: Lectures & Meetings

**Title**: Local systems underlying variation of Hodge structure

**Abstract**: Generalizing finiteness theorems of Parshin, Arakelov, and Faltings, 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. Deligne conjectured that an appropriate form of this finiteness also holds in families of quasiprojective varieties. In the 1990's, Simpson refined this conjecture in the following form: the nonabelian Hodge locus is algebraic. I will discuss joint work with Salim Tayou that these conjectures are true when the algebraic monodromy group is cocompact.