Title: The variety of orthogonal frames
Abstract: Orthogonal frames are tuples of pairwise orthogonal vectors in a quadratic vector space. We study the variety of all orthogonal frames and its defining ideal, and discuss their algebraic, geometric and topological properties. We discuss applications to Lovász-Saks-Schrijver ideals of graphs. Joint work with Alessio Sammartano.
Title: Twisted Artin-Schreier theory
Abstract: Over any field K of characteristic p, we parametrize the (Fₚ ⋊ Fₚˣ)-extensions of K by pairs of elements (g, a) ∈ K×Kˣ using a “twisted” variant of Artin–Schreier theory. Focusing on the case of the local function fields and of the rational function fields K over a finite field of characteristic p, we use this parametrization to study the number of (Fₚ ⋊ Fₚˣ)-extensions of K with prescribed…
Title: Shuffle algebra realization of quantum loop groups
Abstract: In this talk, we shall revise the combinatorial approach to quantum groups in the loop setup. We shall use the interplay of Feigin-Odesskii and formal shuffle algebras that allows to prove Enriquez's conjecture. If time permits, we shall also discuss applications and further generalizations. Based on the joint work with Andrei Negut.
Abstract: This talk is related to the relative Langlands' program, which aims to extend the classical Langlands' program to spherical varieties. In the classical case, a well-known \emph{trace Paley-Wiener theorem} was given by Bernstein, Deligne and Kazhdan in 1986. It gives a characterization of the functions
$$\pi \mapsto \mathrm{Tr}(\pi(f)),$$
with $G$ a reductive $p$-adic group, and where $\pi$ ranges over isomorphism classes of smooth…
