## Speaker:

Liang Xiao

## Speaker Link:

## Institution:

University of Connecticut

## Time:

Tuesday, April 18, 2017 - 2:00pm to 3:00pm

## Location:

RH 340P

The topic of this talk will be understanding the p-adic slopes of modular forms. Recently, Bergdall and Pollack, based on computer calculations, raised a very interesting conjecture on the slopes of overconvergent modular forms, which predicts that the Newton polygons of the characteristic power series of U_p are the same as the Newton polygons of another explicit characteristic power series, which they call ghost series. This conjecture would imply many well-known conjectures regarding slopes of modular forms, like Gouvea's conjecture, Gouvea-Mazur conjecture, and etc. The goal of our joint project is to prove this conjecture under some mild hypothesis, and to explore some further application. I will report on the progress so far.