Title: Strichartz estimates for the Schrödinger equation on the sphere. Abstract: We will discuss Strichartz estimates for solutions of the Schrödinger equation on the standard round sphere, which is related to the results of Burq, Gérard and Tzvetkov (2004). The proof is based on the arithmetic properties of the spectrum of the Laplacian on the sphere […]
Title: Formalizing ∞-Category Theory in Lean Abstract: This semester the category theory seminar will function as a working group with the aim of contributing to an open-source collaborative computer formalization project with the aim of developing the formal theory of ∞-categories in the computer proof assistant Lean. A "blueprint" for the formalization project, which is […]
Title: First explicit reciprocity law for unitary Friedberg—Jacquet periods Abstract: In the early 2000's, Bertolini and Darmon introduced a new technique to bound Selmer groups of elliptic curves via level raising congruences. This was the first example of what is now termed a "bipartite Euler system", and over the last decade we have seen many […]
Title: Geometric Casselman-Shalika in mixed characteristic Abstract: I will present joint work with Ashwin Iyengar and Konrad Zou, where we proved a geometric analog of the (local) Casselman-Shalika formula for split connected reductive groups over mixed characteristic local fields. This formula captures properties of Fourier coefficients of automorphic functions that are fundamental to the Langlands […]
Euler systems and spherical functions. (Continued)