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SUMMARY:Brian Lawrence (UCLA)
DTSTART:20211008T143000Z
DTEND:20211008T160000Z
DTSTAMP:20260423T022622Z
UID:CAFAS/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAFAS/26/">S
 parsity of Integral Points on Moduli Spaces of Varieties</a>\nby Brian Law
 rence (UCLA) as part of Columbia Automorphic Forms and Arithmetic Seminar\
 n\n\nAbstract\nInteresting moduli spaces don't have many integral points. 
  More precisely\, if $X$ is a variety over a number field\, admitting a va
 riation 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 sor
 t of weak generalization of the Shafarevich conjecture\; it is a consequen
 ce of a point-counting theorem of Broberg\, and the largeness of the funda
 mental group of $X$.  Joint with Ellenberg and Venkatesh.\n
LOCATION:https://researchseminars.org/talk/CAFAS/26/
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