Alex Betts (Cornell University)
Event Date
2025-04-11
Event Time
12:00 pm ~ 01:00 pm
Event Location
Wachman Hall 617
Abstract: When you want to solve a Diophantine equation in practice, one of the most powerful modern techniques is the Chabauty—Kim method, which proceeds by constructing p-adic functions vanishing on the rational solutions of your equation. This talk will focus on giving specific examples where we can understand these functions quite explicitly. First, we will explain how to produce abelian integrals vanishing on rational points: the so-called Chabauty—Coleman method. Then we will explain one example going beyond the abelian level: the dilogarithm for once-punctured elliptic curves. This latter is the historical starting point of the quadratic Chabauty method.