Abel in Paris
You are welcome to attend Abel in Paris.
Date: Thursday 11. January 2024
Time: 10am – 4pm
Venue: Centre National de la Recherche Scientifique
Hermite Amphitheatre, Institut Henri Poincaré UAR 839 | Sorbonne Université | CNRS
The event is free, but regestration is requried.
A light lunch will be served.
Sylvie Benzoni, director Institut Henri Poincarè
Lise Øvreås, president the Norwegian Academy of Science and Letters
Helge Holden, chair of the Abel Committee, moderator
10:15-11:15: Yves Meyer
11:30-12:30: Claire Voisin
13:45-14:45 Nalini Anantharaman
15:00-16:00 Martin Hairer
Nalini Anantharaman: On the spectral gap of the laplacian for random hyperbolic surfaces
Although there are several ways to ''choose a compact hyperbolic surface at random'', putting the Weil-Petersson probability measure on the moduli space of hyperbolic surfaces of a given topology is certainly the most natural.
The work of M. Mirzakhani has made possible the study of this probabilistic model: it is one of the only model of ''random riemannian manifolds'' where some explicit calculations are actually possible. One may thus ask questions about of the geometry and the spectral statistics of the laplacian of a randomly chosen surface – in analogy with what is usually asked for models of random graphs.
Nalini Anantharaman will be interested in the spectral gap of the laplacian for a random compact hyperbolic surface, in the limit of large genus (j.w. Laura Monk).
Martin Hairer: Taming infinities
Some physical and mathematical theories have the unfortunate feature that if one takes them at face value, many quantities of interest appear to be infinite! What's worse, this doesn't just happen for some exotic pieces of abstract mathematics, but in the standard theories describing some of the most fundamental aspects of nature. Various techniques, usually going under the common name of "renormalisation" have been developed over the years to address this, allowing mathematicians and physicists to tame these infinities. We will tip our toes into some of the conceptual and mathematical aspects of these techniques and we will see how they have recently been used in probability theory to study equations whose meaning was not even clear until now.
Yves Meyer: Crystalline measures and zeta functions
Claire Voisin: On a problem of Whitney type in algebraic geometry
Whitney embedding theorem in differential geometry says that a small perturbation f' of a map f between two compact manifolds of dimensions m and n (hence f' is isotopic, and a fortiori homotopic to f) is an embedding if n>2m (the Whitney range). I will discuss a related question, asked by Borel and Haefliger, in complex algebraic geometry: can we write the cohomology class of an algebraic subvariety of a smooth projective variety as a combination with integral coefficients of classes of smooth subvarieties? Claire Voisin will discuss classical and recent results on this question, with emphasis on the Whitney range, which has recently been solved in the affirmative by Kollár and herself.