Let G be a semisimple Lie group, e.g. G = SL(n,R). A subgroup Γ of G is called confined if there is a bounded neighborhood of the identity that contains a non-trivial element of every conjugate of Γ. For example, any normal subgroup of a co-compact lattice is confined. In joint work with Tsachik Gelander, we proved that when G has higher rank (e.g. G = SL(n,R) with n>2), a discrete subgroup of G is confined if and only if it is a lattice, which can be seen as an extension of Margulis’ Normal Subgroup Theorem. The proof consists of two independent steps that I hope to explain in my talk: 1) the passage from discrete subgroups to stationary random subgroups and 2) the classification of discrete stationary random subgroups in higher rank. If time permits, I will also discuss some open questions related to this work.

I will present a new theory of motivic cohomology for general (qcqs) schemes. It is related to non-connective algebraic K-theory via an Atiyah-Hirzebruch spectral sequence. In particular, it is non-A1-invariant in general, but it recovers classical motivic cohomology on smooth schemes over a Dedekind domain after A1-localisation. The construction relies on the syntomic cohomology of Bhatt-Morrow-Scholze and the cdh-local motivic cohomology of Bachmann-Elmanto-Morrow, and generalises the construction of Elmanto-Morrow in the case of schemes over a field. 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 seminarIn this talk, we will discuss the classical Ornstein-Zernike theory for the random-cluster models (also known as FK percolation). In its modern form, it is a very robust theory, which most celebrated output is the computation of the asymptotically polynomial corrections to the pure exponential decay of the two-points correlation function of the random-cluster model in the subcritical regime. We will present an ongoing project that extends this theory to the near-critical regime of the two-dimensional random-cluster model, thus providing a precise understanding of the Ornstein-Zernike asymptotics when p approaches the critical parameter $p_c$. The output of this work is a formula encompassing both the critical behaviour of the system when looked at a scale negligible with respect to its correlation length, and its subcritical behaviour when looked at a scale way larger than its correlation length. Based on a joint work with Ioan Manolescu.========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 Cubic CFT can be understood as the O(3) invariant CFT perturbed by a slightly relevant operator. In this paper, we use conformal perturbation theory together with the conformal data of the O(3) vector model to compute the anomalous dimension of scalar bilinear operators of the Cubic CFT. When the Z2 symmetry that flips the signs of φi is gauged, the Cubic model describes a certain phase transition of a quantum dimer model. The scalar bilinear operators are the order parameters of this phase transition. Based on the conformal data of the O(3) CFT, we determine the correction to the critical exponent as η_Cubic-η_O(3)≈ -0.0215(49). The O(3) data is obtained using the numerical conformal bootstrap method to study all four-point correlators involving the four operators: v=φ_i, s=∑_i φ_iφ_i and the leading scalar operators with O(3) isospin j=2 and 4. According to large charge effective theory, the leading operator with charge Q has scaling dimension Δ_Q=c_3/2 * Q^3/2+c_1/2 * Q1^/2. We find a good match with this prediction up to isospin j=6 for spin 0 and 2 and measured the coefficients c_3/2 and c_1/2.  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.

Séminaire informel sur les intersections atypiquesI will recall how understanding the geometry of jumping loci for algebraic cycles in families of smooth projective complex varieties can be reinterpreted as an unlikely intersection problem. I will then present joint work with David Urbanik using this point of view to give sufficient conditions for the analytic density of these loci in the base of the family. ========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.

Period integrals are a fundamental concept in algebraic geometry and number theory. In this talk, we will study the notion of non-archimedean periods as introduced by Kontsevich and Soibelman.  We will give an overview of the non-archimedean SYZ program, which is a close analogue of the classical SYZ conjecture in mirror symmetry. Using the non-archimedean SYZ fibration, we will prove that non-archimedean periods recover the analytic periods for log Calabi-Yau surfaces, verifying a conjecture of Kontsevich and Soibelman. This is joint work with Jonathan Lai.  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. 

Séminaire informel sur les intersections atypiquesThis is part one of a two part lecture, the second of which will be given by Greg Baldi. In the first part we introduce a unified framework for studying « geometric » unlikely intersection problems, which in particular includes all such problems arising from (mixed) Hodge theory, and prove a general geometric Zilber-Pink theorem in this context, subsuming previous results of this nature. The proofs are also effective, in the sense that they give explicit algorithms to compute the relevant atypical loci. In the second part we will explain how this common framework also applies to characterise geometric unlikely intersection phenomena beyond the Hodge-theoretic setting, and in particular to orbit closures in strata of abelian differentials. ========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.

Séminaire informel sur les intersections atypiquesThis is part two of a two part lecture, the first one of which  was  given by David Urbanik. In the first part we introduce a unified  framework for studying « geometric » unlikely intersection problems,  which in particular includes all such problems arising from (mixed)  Hodge theory, and prove a general geometric Zilber-Pink theorem in  this context, subsuming previous results of this nature. The proofs are also effective, in the sense that they give explicit algorithms to compute the relevant atypical loci. In the second part we will explain how this common framework also applies to characterise geometric unlikely intersection phenomena beyond the Hodge-theoretic setting, and in particular to orbit closures in strata of abelian differentials. ========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.

Lattices in semi-simple Lie groups of rank at least 2 — e.g. SL(n,Z) for n>2 — form a class of discrete groups known for having remarkable linear rigidity properties. Notably, their finite dimensional representations are determined by those of the ambient Lie group they live in — e.g. SL(n,R) in the case of SL(n,Z). This is Margulis’ super-rigidity theorem (1974). Motivated by an ergodic version of this theorem, an ambitious program initiated by Gromov and Zimmer in the 1980s aims to understand « non-linear representations » of such lattices into diffeomorphism groups of closed manifolds, or in other words, the differentiable actions of such lattices on closed manifolds.I will first discuss the history and geometric origins of this program. I will then focus on rigidity results about actions of lattices which preserve non-unimodular geometric structures, such as conformal or projective structures, and will mention open directions. The proofs build on recent advances on Zimmer’s conjectures, especially an invariance principle which provides existence of finite invariant measures in various dynamical contexts.

Approximate lattices are discrete subsets of locally compact groups that are an aperiodic generalisation of lattices. They are defined as approximate subgroups (i.e. subsets that are closed under multiplication up to a finite multiplicative error) that are discrete and have finite co-volume. They were first studied by Yves Meyer who classified them in locally compact abelian groups by means of the so-called « cut-and-project schemes ». Approximate lattices were subsequently used to model a diversity of objects such as aperiodic tilings (Penrose and the « hat »), Pisot numbers, and quasi-crystals.In non-abelian groups, however, their structure remained mysterious. I will explain how the structure of approximate lattices in linear algebraic groups can be understood thanks to a notion of cohomology that sits halfway between bounded cohomology and the usual cohomology, thus generalising Meyer’s theorem. Along the way, we will talk about Pisot numbers, extending a theorem of Lubotzky, Mozes and Raghunathan, amenability and (some) model theory.

Séminaire informel sur les intersections atypiquesI will present some recent results obtained with  Andrei Yafaev on André-Pink-Zannier and generalised Hecke orbits in Shimura varieties, such as moduli spaces of abelian varieties. ========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 discuss Langevin dynamics of N particles on Rd interacting through a singular repulsive potential, such as the Lennard-Jones potential, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance.  The proof relies on an explicit construction of a Lyapunov function using a modified Gamma calculus (Bakry-Emery).  In contrast to previous results for such systems, our results imply geometric convergence to equilibrium starting from an essentially optimal family of initial distributions. This is based on joint work with F.Baudoin and D.Herzog.========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.