Title: Syzygies of adjoint linear series on projective varietiesAbstract: Syzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. Starting with the pioneering work of Mark Green on curves, numerous attempts have been made to extend these results to higher dimensions. Ein and Lazarsfeld proved that if A is a very ample […]
Title: Kloosterman sums in representation theory of GL(n, Fq) Abstract: Given a "nice" irreducible representation of GL(n, Fq), one can define a special matrix coefficient attached to it, called the Bessel function. Often Kloosterman sums show up as special values of these Bessel functions. In this talk, I will first explain my previous results regarding […]
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Title: An introduction to pretorsion theories (based on the collaboration with Alberto Facchini, Carmelo Finocchiaro, Francis Borceux, Federico Campanini, Aline Michel and Walter Tholen) Abstract: The notion of pretorsion theory is a natural extension of the classical notion of torsion theory in an abelian category. The idea is to associate, with any pair (T , F) […]
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 […]