researchseminars.org

Brian Lawrence (UCLA)
2022-04-28 21:00 - 22:00 UTC | https://researchseminars.org/talk/UCSD_NTS/61/
Title: Sparsity of Integral Points on Moduli Spaces of Varieties (https://researchseminars.org/talk/UCSD_NTS/61/)
by Brian Lawrence (UCLA) as part of UCSD number theory seminar

Lecture held in APM 6402 and online.

Abstract
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.

pre-talk at 1:20pm
