There will be two seminars on February 12, from 2:30 – 3:30pm and from 4 – 5pm.
Masato Kurihara (Keio University)
Title: Higher Fitting ideals of arithmetic objects
Abstract: I will talk about structure theorems on the Selmer group of an elliptic curve, which describe the structure by modular symbols. In the latter half, I will talk on a part of our recent joint work with D. Burns and T. Sano where for any finite abelian extension with Galois group G, the higher Fitting ideals of the class group as a G-module are studied.
Thanasis Bouganis (Durham)
Title: p-adic measures for Hermitian modular forms and the Rankin-Selberg method
Abstract: In this talk we will discuss the construction of p-adic measures for Hermitian modular forms (modular forms associated to unitary groups). For the construction of such measures there exist two general approaches. The first (an ongoing project of Eischen, Harris, Li and Skinner) is based on the doubling-method. The second is based on Rankin-Selberg integrals involving theta series. In this talk we will report on our work on developing this second approach. We will also discuss the similarities and differences to the Siegel modular forms situation (modular forms attached to symplectic groups), where the Rankin-Selberg method has been studied in relation to p-adic measures by Panchishkin and the doubling-method by Boecherer and Schmidt.