January 12, 2023
TITLE: Quantum gravity conjectures and asymptotic Hodge theory
ABSTRACT: In this talk I will explain how asymptotic Hodge theory can be used to provide general evidence for some of the quantum gravity conjectures. In particular, I will describe how the orbit theorems of Hodge theory can be used in addressing the so-called Distance Conjecture. For Calabi-Yau manifolds, I will sketch the implied classification of asymptotic regions of the moduli space and comment on the special properties of infinite distance boundaries. I will highlight that the quantum gravity conjectures can actually lead to new mathematical theorems by presenting a finiteness theorem generalizing a famous result of Cattani, Deligne, and Kaplan on Hodge classes. This new result is based on work with B. Bakker, C. Schnell, and J. Tsimerman.