Michigan State University
When
2 – 3 p.m., March 18, 2026
Where
Title: Minimal lifts of modular forms in characteristic three
Abstract: Given an irreducible two-dimensional mod-p Galois representation, Serre's conjecture tells you whether or not it arises as the mod-p Galois representation of a modular form. Even better, Serre gave a precise prediction for minimal weight, level, and character of such a modular form.
When p is 2 or 3, the original form of the conjecture was slightly off in the character part and Serre himself gave counterexamples. I'll talk about a situation where there's a notion of "minimal" that is not captured by the weight, level, and character, and how Serre's counterexamples relate to this situation. This is joint work with Patrick Allen.