Time: June 20, 22, 10-12

In this joint work in progress with Ruochuan Liu, we investigate the slopes of modular forms, namely the p-adic valuations of Up-eigenvalues of modular forms. We aim to prove the ghost conjecture made by Bergdall and Pollack, which gives an explicit recipe to generate the slopes of all modular forms under certain regularity conditions. 

In the first talk, L.X. will first state the local version of ghost conjecture and explain the general strategy; in the second talk, B.Z. will explain how one can try to prove it in a special case.