I will give several definitions of entropy at infinity for a dynamical system on a noncompact topological space. In the case of geodesic flows in negative curvature, in joint work with S. Gouëzel and S. Tapie, we showed that these definitions coincide. When the entropy at infinity is strictly smaller than the topological entropy, we obtained numerous interesting applications in the past few years. In a more recent work with A. Florio and A. Vaugon, we are able to prove that some of these properties still hold in the generality of hyperbolic flows on noncompact manifolds. I will try to give the flavour of these works.

Balzan Lectures on 50 Years of Binary Pulsars
The first  pulsar in a binary system (PSR B1913+16) was discovered in the summer of 1974 by Russell Hulse and Joseph Taylor. In the fifty years since this pioneering discovery, many more binary pulsars were discovered, including remarkable systems such as the double binary pulsar PSR J0737−3039A/B (with two active radio pulsars detectable  from the Earth), and the triple system PSR J0337+1715. Binary pulsars have triggered many research works in theoretical gravity, and have opened up new experimental windows on relativistic gravity. The comparison between binary-pulsar timing data and theoretical predictions has notably provided the first  direct observational proof that  gravity propagates at the velocity of light, and the first accurate tests of the strong-field regime of relativistic gravity.
To celebrate 50 years of binary-pulsar physics, two complementary Balzan lectures will present reviews of: (1) the theoretical works triggered by the discovery of binary pulsars; and (2) the state-of-the-art of binary pulsar observations and of their scientific content.
Supported by the « 2021 Balzan Prize for Gravitation: Physical and Astrophysical Aspects », awarded to Thibault Damour

Balzan Lectures on 50 Years of Binary Pulsars
The first  pulsar in a binary system (PSR B1913+16) was discovered in the summer of 1974 by Russell Hulse and Joseph Taylor. In the fifty years since this pioneering discovery, many more binary pulsars were discovered, including remarkable systems such as the double binary pulsar PSR J0737−3039A/B (with two active radio pulsars detectable  from the Earth), and the triple system PSR J0337+1715. Binary pulsars have triggered many research works in theoretical gravity, and have opened up new experimental windows on relativistic gravity. The comparison between binary-pulsar timing data and theoretical predictions has notably provided the first  direct observational proof that  gravity propagates at the velocity of light, and the first accurate tests of the strong-field regime of relativistic gravity.
To celebrate 50 years of binary-pulsar physics, two complementary Balzan lectures will present reviews of: (1) the theoretical works triggered by the discovery of binary pulsars; and (2) the state-of-the-art of binary pulsar observations and of their scientific content.
Supported by the « 2021 Balzan Prize for Gravitation: Physical and Astrophysical Aspects », awarded to Thibault Damour

Probability and analysis informal seminar
Tensor networks are a recent cool addition to physicist’s toolkit used to study renormalization of lattice models. However the mathematical theory of tensor network renormalization group (TNRG) is still in its infancy. I will aim to transmit my excitement about the tensor networks. Rough plan:1. Wilson’s conjecture about renormalization group fixed points describing criticality – can we prove it?2. Why are tensor networks better than other approaches to renormalization (e.g. spin blocking).3. Numerical algorithms for TNRG – what do people see numerically?4. Discrete scaling operator 5. A few mathematically rigorous results about TNRG6. Open problems
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Séminaire de géométrie arithmétique
The notion of micro support in mixed characteristic is formulated using the Frobenius–Witt cotangent bundle but the existence of the singular support is not yet known. We introduce a relative notion of micro support over a fixed regular scheme S and prove the existence of a saturation of the relative singular support on  smooth schemes over S. The proof is a variation of that by Beilinson using the Radon transform.
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I will discuss how M2-M5 intersections in the twisted M-theory background yield R-matrices of quantum toroidal algebra of gl(1). These intersections are also identified as Miura operators, providing the Miura transformation for the q-deformed W- and Y-algebras. Consequently, the intertwining relation of the q-deformed Maulik-Okounkov R-matrix is illuminated as a Yang-Baxter equation, in particular. Also, I will explain the M2-M5 intersection (equivalently the Miura operator) gives rise to the qq-characters of the 5d N=1 gauge theory, illuminating an algebraic meaning of the latter.
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I will discuss two lattice avatars of ’t Hooft anomalies. The first one involves an action of a symmetry group on observables of a 1d spin system. It is related to a generalization of the Lieb-Schultz-Mattis theorem. The second one concerns symmetries of gapped states of spin systems. I will argue that the Hall conductance and other topological invariants of symmetric gapped states can be interpreted as obstructions to localizing the symmetry even approximately.  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.

Probability and analysis informal seminarIn this joint talk we focus on some recent results on packings of identical hard spheres of diameter D on 2D- and 3D- lattices and graphs (a unit triangular lattice A2, a unit honeycomb graph H2, a unit square lattice Z2, a unit cubic lattice Z3). In particular, we will use connections with the algebraic number theory. Our results identify dense-packing configurations and their random « perturbations » (extreme Gibbs distributions) describing high-density « pure phases » of the hard-sphere lattice model of statistical mechanics. ========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 seminarThis talk presents a quantitative homogenization for non-gradient exclusion process. The main strategy roots from the quantitative homogenization theory developed by Armstrong, Kuusi, Mourrat and Smart, and was already implemented in the previous work by Giunti-Gu-Mourrat’ 22 in an interacting particle system without exclusion. The new challenges here come from the hard core constraint of the particle number and the curse of dimension, and I will explain how to overcome them by a new coarse-grained strategy.  As an application, our result can be integrated into the classical work Funaki-Uchiyama-Yau’ 96 and yield a quantitative hydrodynamic limit. This talk is based on a joint work with Tadahisa Funaki (BIMSA) and Han Wang (Qiuzhen College, Tsinghua University).========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 seminarClassical spin models taking value in the circle are naturally dual to spin models taking value in the integers (on the dual graph). Unlike in the context of Ising/Potts models, this duality is only visible at the level of order-disorder operators, there are no bijections between the models (as far as we know). I will revisit these well known relations, and will argue how the continuous symmetry group of S^1 will help to prove different results for the spin model and dual height function model. Notably, I will show a type of Gaussian domination holds for the height function on any graph, I will mention how it can be used to prove the Berezinskii–Kosterlitz–Thouless transition and time permitting, I will present some other results. All is based on joint work with Marcin Lis.  ========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 seminarI will talk about the eigenvalue asymptotics of the Laplace-Beltrami operator for certain singular Riemannian metrics. This is motivated by the study of propagation of soundwaves in gas planets. It is joint work in progress with Yves Colin de Verdière, Maarten de Hoop and Emmanuel Trélat.========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.

We use holography to study the large spin J limit of the spectrum of low energy states with charge Q under a U(1) conserved current in CFTs in d>2 dimensions, with a focus on d=3 and d=4. For Q=2, the spectrum of such states is known to be universal and properly captured by the long-distance limit of holographic theories, regardless of whether the CFT itself is holographic. We study in detail the holographic description of such states at Q>2, by considering the contribution to the energies of Q scalar particles coming from single photon and graviton exchange in the bulk of AdS; in some cases, scalar exchange and bulk contact terms are also included. For a range of finite values of Q and J, we numerically diagonalize the Hamiltonian for such states and examine the resulting spectrum and wavefunctions as a function of the dimension Δ of the charge-one operator and the central charges cT, cJ of the stress tensor and U(1) current, finding multiple regions in parameter space with qualitatively different behavior. We discuss the extension of these results to the regime of parametrically large charge Q, as well as to what extent such results are expected to hold universally, beyond the limit of holographic CFTs. We compare our holographic computations to results from the conformal bootstrap for the 3d O(2) model at Q=3 and Q=4 and find excellent agreement. 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.