## Algebra

•  Brian Lawrence, UCLA
•  Sparsity of Integral Points on Moduli Spaces of Varieties (in person!)
•  04/20/2022
•  4:00 PM - 5:00 PM
•  C304 Wells Hall
•  Preston Wake (wakepres@msu.edu)

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

## Contact

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Michigan State University
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College of Natural Science