One of the celebrated outcomes of the modern conformal bootstrap is that most likely the 3D Ising model is an (extremal) conformal field theory (CFT) that saturates the bound in a certain optimization problem. However, numerically, we don’t see the different families of operators predicted from the lightcone analysis of a single crossing equation. This raises questions about whether extremal CFTs have a sparser spectrum than predicted or if numerics in the derivative basis face challenges in capturing these additional operators. This motivates us to seek an alternative basis of functionals acting on a single correlator crossing equation. These functionals are constructed using a class of 1D functionals that are dual to generalized free-field solutions. We took the first modest step to implement these functionals to numerically bootstrap higher-dimensional CFTs, demonstrating their efficiency, especially in two dimensions, where they outperform the traditional approach. Additionally, we have identified a series of new kinks in our plot that have gone unnoticed so far. In three dimensions, we reproduced the known bound, and although it is efficient, we require better control over the evaluation of these functionals to progress further. Notably, the convergence of these bounds is also better for large external dimensions in this functional basis. In this talk, I will provide an overview of this framework and discuss the general outlook.  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_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

We consider a finitely generated, Zariski dense, Anosov subgroup of SL(d,R), d>2. We discuss results and problems about the dimension of the unique minimal set for the action of the group on partial flag spaces.

The notion of Hp,q-convex cocompact representations was introduced by Danciger, Guéritaud, and Kassel and provides a unifying framework for several interesting classes of discrete subgroups of the orthogonal groups SO(p,q+1), such as holonomies of convex cocompact hyperbolic manifolds or maximal globally hyperbolic anti-de Sitter spacetimes of negative Euler characteristic. By recent works of Seppi-Smith-Toulisse and Beyrer-Kassel, we now know that any Hp,q-convex cocompact representation of a group Γ of cohomological dimension p admits a unique invariant maximal spacelike p-dimensional manifold inside the pseudo-Riemannian hyperbolic space Hp,q, and that the space of Hp,q-convex cocompact representations of Γ forms a union of connected components in the associated SO(p,q+1)-character variety.In this talk, I will describe some recent joint work with Gabriele Viaggi in which we provide various applications for the existence of invariant maximal spacelike submanifolds. These include a rigidity result for the pseudo-Riemannian critical exponent (which answers affirmatively a question of Glorieux-Monclair), a comparison between entropy and volume, and several compactness and finiteness criteria in this framework.

The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning, and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics, and problems of scientific reproducibility will be presented. This workshop is particularly intended for doctoral and post-doctoral researchers.Registration is free and open until March 27, 2024.Invited speakers:Stephan Clémençon (LTCI/Télécom Paris/Insitut Polytechnique de Paris)Luca Ganassali (LMO/Université Paris-Saclay)Marine Le Morvan (SODA/INRIA Saclay)Erwan Le Pennec (CMAP/École polytechnique)Gilles Stoltz (CNRS/LMO/Université Paris-Saclay)Maria Vakalopoulou (MICS/Centralesupélec)Organizers: Evgenii Chzhen (Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay)Florence Tupin (LTCI/Télécom Paris)

Seminar on Quantum Modularity and ResurgenceQuantizing the mirror curve of a toric Calabi-Yau threefold gives rise to quantum-mechanical operators. Their fermionic spectral traces produce factorially divergent power series in the Planck constant and its inverse, which are conjecturally captured by the Nekrasov-Shatashvili and standard topological strings via the TS/ST correspondence. In this talk, I will discuss a general conjecture on the resurgence of these dual asymptotic series, and I will present a proven exact solution in the case of the first spectral trace of local $P^2$. A remarkable number-theoretic structure underpins the resurgent properties of the weak and strong coupling expansions and paves the way for new insights relating them to quantum modular forms. Finally, I will mention how these results fit into a broader paradigm linking resurgence and quantum modularity. This talk is based on arXiv:2212.10606 and further work with V. Fantini (available soon).========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.

Dark compact objects are nowadays routinely observed through multiple experimental schemes. Measurements of their vibrational spectra offer unprecedented opportunities to investigate the highly dynamical regime of General Relativity, search for signs of new physics, and increase the evidence for their « black hole nature ». After an introduction to the topic, I will review recent achievements of this scientific program enabled by gravitational-wave observations, and current efforts to extend it through the inclusion of nonlinear effects and generic orbital configurations of binary mergers. Prospects for high-precision measurements through next-generation interferometric detectors will also be briefly discussed.[1] https://drive.google.com/file/d/1OcfmyL0KBUAZrXfi9N7dhiOaALbyEgxj/view?usp=sharing 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_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.   

A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.   

A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.   

A modern perspective on symmetry in quantum theories identifies the topological invariance of a symmetry operator within correlation functions as its defining property. In addition to suggesting generalised notions of symmetry, this viewpoint enables a calculus of topological defects, which has a strong category-theoretic flavour, that leverages well-established methods from topological quantum field theory. Focusing on finite symmetries, I will delve during these lectures into a realisation of this program in the context of one-dimensional quantum lattice models. Concretely, I will present a framework for systematically investigating lattice Hamiltonians, elucidating their symmetry operators, defining duality/gauging transformations and computing the mapping of topological sectors through such transformations. Moreover, I will comment on the classification of gapped symmetric phases for generalised symmetry and the construction of the corresponding order/disorder parameters. I will provide explicit treatments of familiar physical systems from condensed matter theory, shedding light on celebrated results and offering resolutions to certain open problems. Time permitting, I will briefly touch upon generalisations to higher dimensions and implications to numerical simulations.   

We start with reminding  basic molecular structures (Crick dogma, genetic code etc.) in living  entities and classical  examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy  on the nature of Life. Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current  and projected numerical data on the human role in ecology of Earth.

We start with reminding  basic molecular structures (Crick dogma, genetic code etc.) in living  entities and classical  examples of the mathematical thought in genetic (Darwin, Mendel, Morgan, Sturtevant, trees of sequences…) and the traditional discussion/controversy  on the nature of Life. Then we present a mathematical counterpart to the question “What is Life?”, indicate possible role of mathematics in the future bioengineering and conclude with the current  and projected numerical data on the human role in ecology of Earth.