Event time:

Tuesday, April 26, 2022 - 4:30pm

Speaker:

Brian Lawrence

Speaker affiliation:

UCLA

Event description:

Interesting moduli spaces don't have many integral points. More precisely, if X is a variety over a number field, admitting a variation of Hodge structure whose associate period map is injective, then the number of S-integral points on X of height at most H grows more slowly than $H^{\epsilon}$, for any positive $\epsilon$. This is a sort of weak generalization of the Shafarevich conjecture; it is a consequence of a point-counting theorem of Broberg, and the largeness of the fundamental group of X. Joint with Ellenberg and Venkatesh.

Research Area(s):