Seminar: Analytical study of Poincaré series

Seminar: Analytical study of Poincaré series

Thời gian: 09:00 đến 11:00 Ngày 17/08/2026

Địa điểm: Phòng C101, VIASM

Abstract: 

I will start by discussing the growth of lattice points in the dilation of a convex subset of the Euclidean space. This problem naturally gives rise to a ”length spectrum” to which we can associate Poincaré series. My goal is to explain first on this simple geometric model how the study of these zeta functions (or of the related couting problem) can be understood as a problem in dynamical systems. More precisely, they can be transferred into the analytic study of certain flows acting on the unit tangent bundle of the torus. Once this first problem is discussed, I will focus on the extension of these questions to negatively curved manifolds and discuss the relation of Poincaré series with certain topological invariants (Euler characteristic, linking number of knots for instance). 

Nguyen Viet Dang is a Professor at Institut de Recherche Mathématiques Avancées, Université de Strasbourg. He obtained his PhD from Université de Paris in 2013, and defended his Habilitation at Université Paris Saclay in 2021. He has been a junior member of the Institut Universitaire de France since 2022 and professor at Institut Mathématique de Jussieu Sorbonne University from 2021-2024. He works on applications of methods from harmonic and microlocal analysis to dynamical systems and quantum field theory.

nguyen-viet-dang.png