Alex Betts (Cornell University)
Event Date
2025-04-11
Event Time
04:00 pm ~ 05:00 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. In this talk, I will discuss a heuristic which predicts when these functions cut out exactly the set of rational points. As we will see, the naive version of the heuristic is not quite correct, since there can occasionally be extra "unexpected" algebraic irrational points where the functions vanish (in accordance with a conjecture of Stoll). I will outline what is known about these unexpected points, including some ongoing work with Jennifer Balakrishnan.