Study group on eigenvarieties

General information: In this study group, we are going to learn about the construction of eigenvarieties. We shall start with basic discussions on nonarchimedean functional analysis. The preparation of nonarchimedean functional analysis then allows one to construct the so-called spectral variety. Then, we shall learn about Buzzard's eigenvariety machinery. At the end of the study group, we shall see how eigenvarieties are used in modern number theory. This study group is co-organised with Muhammad Manji. 

Time: Thursdays, 3 pm

Room: B1.01

Schedule

Talk 1 (12. Jan.): Introduction. Speaker: Ju-Feng

Talk 2 (19. Jan): Nonarchimedean functional analysis (over a nonarchimedean field). Speaker: Alex

Banach modules, Buzzard's (Pr) condition, compact operators.

Talk 3 (26. Jan.): Nonarchimedean functional analysis (over an affinoid algebra). Speaker: Muhammad

Banach modules, Buzzard's (Pr) condition, compact operators.

Talk 4  (02. Feb.): Fredholm determinant and the spectral variety. Speaker: Arshay

Fredholm determinant, slope decomposition, spectral varieties.

Talk 5 (09. Feb.): Buzzard's eigenvariety machinery. Speaker: Arshay

Buzzard's eigenvariety machinery, properties of eigenvarieties.

Talk 6 (16. Feb.): Stevens's overconvergent modular symbols I. Speaker: James

Classical and overconvergent modular symbols, Eichler--Shimura decomposition, Stevens's control theorem.

Talk 7 (23. Feb.): Stevens's overconvergent modular symbols II. Speaker: James

Classical and overconvergent modular symbols, Eichler--Shimura decomposition, Stevens's control theorem.

Talk 8 (02. Mar.): Application to p-adic L-functions. Speaker: Pak-Hin (cancelled)

Reference