Thesis Oral Defense/AAG Seminar: Hodge classes in the cohomology of local system

Speaker: Xiaojiang Cheng, Washington University in St. Louis

Abstract: Let $S$ be an arithmetic quotient of a Hermitian symmetric domain and $X/S$ be a family of varieties over $S$. One interesting problem is to find the Hodge classes of $XS, and if possible, to prove the Hodge conjecture for $X$.  Using techniques from automorphic forms, we studied the Hodge conjecture for certain families of varieties over arithmetic quotients of balls and the Siegel domain of degree two. As a byproduct, we derived formulas for Hodge numbers in terms of automorphic forms.

Advisor: Matt Kerr