Serre's conjecture and two notions of minimal weight

Abstract: The strong form of Serre's conjecture states that every two-dimensional continuous, odd, irreducible mod $p$ Galois representation arises from a modular form of a specific minimal weight, level and character. We will see how one can use modular representation theory to prove the minimal weight is equal to a notion of minimal weight inspired by the recipe for weights introduced by Buzzard, Diamond and Jarvis. We will also briefly touch on generalisations of this, again using modular representation theory, which is the subject of work in progress.

number theoryrepresentation theory

Audience: researchers in the topic

Cross Atlantic Representation Theory and Other topics ONline (CARTOON) conference