Chabauty's method and effectivity in Diophantine geometry

Chabauty's method and effectivity in Diophantine geometry

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Gyujin Oh, Princeton University
Fine Hall 110

I will talk about the method of Chabauty, an approach towards Siegel's finiteness theorem and Mordell's conjecture, whose idea is along the lines of those of Weil and Lang. Extended by Coleman, the method of Chabauty can produce good estimates on the number of rational points on a higher genus curve in certain cases. We will in particular see that it sometimes provides us a sharp bound via some simple and explicit calculation of p-adic integrals. Time permitting, I would want to discuss the non-linear analogue of Chabauty's method developed by Kim, and also the hope that this can give an effective approach to Mordell's conjecture, if one believes some well-renowned conjectures of anabelian and/or motivic nature.