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Berkeley-Caltech-Stanford Joint Number Theory Seminar

Monday, November 8, 2021
12:30pm to 1:30pm
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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.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].