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Monday, November 08, 2021
12:30 PM - 1:30 PM
Online Event

# Berkeley-Caltech-Stanford Joint Number Theory Seminar

Sparsity of Integral Points on Moduli Spaces of Varieties
Brian Lawrence, Department of Mathematics, UCLA,

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.
https://arxiv.org/abs/2109.01043