Atttention : La première Leçon aura lieu à l’Institut Mathématique d’Orsay, Amphi Yoccoz, le 15 mai à 14hRetrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :https://fondation-hadamard.fr/en/articles/2023/01/20/hadamard-lectures-2023/Abstract:Since Weil, mathematicians have understood that there is a deep analogy between the ordinary integers and polynomials in one variable over a finite field, as well as between number fields and the fields of functions on algebraic curves over finite fields. Using this, we can take classical problems in number theory and consider their analogues involving polynomials over finite fields, to which new geometric techniques can be applied that aren’t available in the classical setting. In this course, I will survey recent progress on such problems.Specifically, I will try to highlight how the geometric perspective produces connections to other areas of mathematics, including how the circle method for counting solutions to Diophantine equations can be used to study the topology of moduli spaces of curves in varieties, how geometric approaches to the Cohen-Lenstra heuristics and their generalizations motivate new results of a purely probabilistic nature, and how the analytic theory of automorphic forms over function fields is connected to geometric Langlands theory.

Atttention : La première Leçon aura lieu à l’Institut Mathématique d’Orsay, Amphi Yoccoz, le 15 mai à 14hRetrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :https://fondation-hadamard.fr/en/articles/2023/01/20/hadamard-lectures-2023/Abstract:Since Weil, mathematicians have understood that there is a deep analogy between the ordinary integers and polynomials in one variable over a finite field, as well as between number fields and the fields of functions on algebraic curves over finite fields. Using this, we can take classical problems in number theory and consider their analogues involving polynomials over finite fields, to which new geometric techniques can be applied that aren’t available in the classical setting. In this course, I will survey recent progress on such problems.Specifically, I will try to highlight how the geometric perspective produces connections to other areas of mathematics, including how the circle method for counting solutions to Diophantine equations can be used to study the topology of moduli spaces of curves in varieties, how geometric approaches to the Cohen-Lenstra heuristics and their generalizations motivate new results of a purely probabilistic nature, and how the analytic theory of automorphic forms over function fields is connected to geometric Langlands theory.

Let M be a geometrically finite hyperbolic manifold, that is, a hyperbolic manifold with a fundamental domain consisting of a finitely-sided polyhedron. There exists a unique measure on the unit tangent bundle invariant under the geodesic flow with maximal entropy, and we consider its lift to the frame bundle. In joint work with Pratyush Sarkar and Wenyu Pan, we prove that the frame flow is exponentially mixing with respect to this measure. To establish exponential mixing, we base ourselves on the countable coding of the flow and a version of Dolgopyat’s method, à la Sarkar-Winter and Tsujii-Zhang. To overcome the difficulty of the fractal structure in applying Dolgopyat’s method, we prove a large deviation property for symbolic recurrence to the large subsets.

We study the problem of determining when a compact group can be realized as the group of isometries of a norm on a finite-dimensional real vector space. This problem turns out to be difficult to solve in full generality, but we manage to understand the connected groups that arise as connected components of isometry groups. The classification we obtain is related to transitive actions on spheres (Borel, Montgomery-Samelson) on the one hand and to prehomogeneous spaces (Vinberg, Sato-Kimura) on the other. Joint work with Martin Liebeck, Assaf Naor and Aluna Rizzoli.

I will give new non-commutative (matrix model) membrane solutions, and discuss the issue of infinite-energy extended objects sweeping out in space-time world-volumes of vanishing mean curvature.  Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide. 

Probability and analysis informal seminarThe 2D XY model has attracted attention of physicists and mathematicians for several decades. One way to understand this model is through its dual height function. Recent developments make it possible to show that the phase transitions of the two models coincide. At the core of the proof is a new perspective on the Symanzik/Brydges–Fröhlich–Spencer random walk. The talk is based on arXiv:2301.06905 (Bijecting the BKT transition) and arXiv:2211.14365 (A dichotomy theory for height functions).  ========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Probability and analysis informal seminarWe consider supercritical bond percolation on $Z^d$ and study the chemical distance, i.e., the graph distance on the infinite cluster. It is well-known that there exists a deterministic constant μ(x) such that the chemical distance D(0,nx) between two connected points 0 and nx grows like nμ(x). We prove the existence of the rate function for the upper tail large deviation event {D(0,nx)>nμ(x)(1+ϵ),0↔nx} for d>=3.  Joint work with Shuta Nakajima.  ========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

I will discuss explicit M(em)-brane solutions (including some non-commutative ones), relations to hydrodynamics, singularity-formation, and aspects of integrability  Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide. 

Le théorème de comparaison est un sujet classique en théorie de Hodge p-adique. Récemment, Guo et Reinecke ont montré un théorème de comparaison p-adique pour les systèmes locaux cristallins en utilisant la théorie de cohomologie prismatique de Bhatt-Scholze. Un des points clés de leur travail est d’établir un théorème de comparaison étale-prismatique pour les systèmes locaux cristallins. Dans cet exposé, j’expliquerai une nouvelle approche à la comparaison étale-prismatique, qui marche bien aussi dans le cas semi-stable.   Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide. 

Nash’s geometric ideas in PDE have returned to the prominence due to their role in the solution of Onsager’s conjecture on energy conservation in the Euler equation and counterexamples to regularity of non-linear elliptic equations.The first lecture will contain an elementary introduction to the basic geometric techniques and results starting from a short geometric proof of the C1-isometric immersion and related theorems.The second lecture will survey more recent results, ideas and techniques. Veuillez cliquer sur le lien ci-dessous afin de rejoindre le webinaire : https://us02web.zoom.us/j/81163611896?pwd=T043TzNvZnpUbUNiSE1BM0FBa05RQT09 Code secret : 822885 Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide. 

Nash’s geometric ideas in PDE have returned to the prominence due to their role in the solution of Onsager’s conjecture on energy conservation in the Euler equation and counterexamples to regularity of non-linear elliptic equations.The first lecture will contain an elementary introduction to the basic geometric techniques and results starting from a short geometric proof of the C1-isometric immersion and related theorems.The second lecture will survey more recent results, ideas and techniques. Veuillez cliquer sur le lien ci-dessous afin de rejoindre le webinaire : https://us02web.zoom.us/j/81163611896?pwd=T043TzNvZnpUbUNiSE1BM0FBa05RQT09 Code secret : 822885 Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide. 

The frame flow over negatively-curved Riemannian manifolds is a historical example of a partially hyperbolic dynamical system. Excluding some obvious counterexamples such as Kähler manifolds, its ergodicity was conjectured by Brin in the 70s. While it has been known since Brin-Gromov (1980) that it is ergodic on odd-dimensional manifolds (and dimension not equal to 7), the even-dimensional case is still open. In this talk, I will explain recent progress towards this conjecture: I will show that in dimensions 4k+2 the frame flow is ergodic if the Riemannian manifold is 0.27 pinched (i.e., the sectional curvature is between -1 and -0.27), and in dimensions 4k if it is 0.55 pinched. This problem turns out to be surprisingly rich and at the interplay of different fields: (partially) hyperbolic dynamical systems, algebraic topology (classification of topological structures over spheres), Riemannian geometry and harmonic analysis (Pestov identity and microlocal analysis). Joint work with Mihajlo Cekić, Andrei Moroianu, Uwe Semmelmann.