Abstract: We show that the Bergman kernel of a finite volumequotient of a Hermitian manifold $\wi{X}$ with bounded geometry by a discrete group $\Gamma$ of its isometries identifies with the averaging over $\Gamma$ of the Bergman kernel on $\wi{X}$. We then give applications to the existence of Poincaré series, extending a result of Kollar to the case of finite volume quotients. This is a joint work with Louis Ioos, Wen Lu and Xiaonan Ma.
Bei…
Title: An Extension of Sato-Kimura Theorem for Semi-invariant rings
Abstract: We prove an analog of a theorem of Sato–Kimura for semi-invariant rings arising from representations of finite-dimensional algebras over an algebraically closed field K of characteristic 0. Assuming the coordinate ring is factorial and the representation variety has generic orbits of codimension one, we show that the semi-invariant ring is a complete intersection and…
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…
