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Presented By: Group, Lie and Number Theory Seminar - Department of Mathematics

GLNT: Mazur's Program B and the geometry of rational points

Ari Shnidman (Temple University)

I'll describe recent progress on Mazur's Program B over Q, which aims to classify all rational points on all modular curves. Conditional on an effective version of Serre's uniformity conjecture due to Zywina, we give such a classification. Using our parameterization we try to answer the following question inspired by Ogg: to what extent do rational points on modular curves come from geometry? This is joint work with Maarten Derickx, Sachi Hashimoto, and Filip Najman.

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