##### Department of Mathematics,

University of California San Diego

****************************

### Food for Thought

## Jianxiang Tan

#### UCSD

## The Spectral Halo Conjecture

##### Abstract:

The eigencurve is an important object in the study of p-adic families of modular forms, yet many of its geometric structures remain mysterious. I will give an elementary introduction to the theory of p-adic modular forms and the construction of eigencurve. Then we will take a glance at this beautiful conjecture.

### May 10, 2023

### 1:00 PM

HSS 4025

****************************