Title: Galois theory and homology in quasi-abelian functor categories Abstract: The aim of this talk is to give an introduction to the categorical theory of (higher) central extensions and of generalized Hopf formulae for homology, and to apply these methods to the study of, in particular, the category Grpdn(A) of internal n-fold groupoids in a […]
Euler systems and spherical functions.
Title: Cohomological splitting of fibrations over rationally connected basesAbstract: A classical result of Blanchard and Deligne asserts that the rational cohomology of a smooth projective fibration splits additively. In this talk, I will discuss how to prove an analogous result for cohomology with coefficients in fields of positive characteristics. Although the splitting in this setting does not […]
Langlands functoriality and stable transfer.
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)
Title: The geometry and topology of lower bounds on scalar curvatureAbstract: In this talk, I will discuss some recent results about controlling the geometry and topology of manifolds from a (positive) lower bound on their scalar curvature.
Title: Curves on Varieties and the Degree of Irrationality.Abstract: Inspired by the Noether-Lefschetz theorem, it has been conjectured that the degree of any curve on a (very) general complete intersection variety is divisible by the degree of the variety itself. In this talk, we present a weaker version of this conjecture. Using this result, we confirm a […]