# Algebra/Number Theory Seminar

## Towards a classification of adelic Galois representations attached to elliptic curves over $\mathbb{Q}$.

Alvaro Lozano-Robledo (UConn)

Thursday, March 11th, 2021
2:00 PM - 3:00 PM
https://rochester.zoom.us/j/98805708475

Let $E$ be an elliptic curve defined over $\mathbb{Q}$. The adelic Galois representation attached to $E$ (this object will be defined during the talk) captures all sorts of interesting information about the arithmetic of the points on $E(\overline{\mathbb{Q}})$, including data about the torsion subgroup, isogenies, and other finer invariants of the curve and its isogeny class. In this talk, we will give a summary of recent results towards the classification (up to isomorphism) of the possible adelic Galois representations that arise from elliptic curves over $\mathbb{Q}$, and present some recent results of the author and his collaborators (Garen Chiloyan, Harris Daniels, Jackson Morrow) in this area.

Event contact: c dot d dot haessig at rochester dot edu