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