Seed Seminar of Mathematics and Physics
 
Lipschitz transport maps between two measures are useful tools for transferring analytical properties, such as functional inequalities. The most well-known result in this field is Caffarelli’s contraction theorem, which shows that the optimal transport map from a Gaussian to a uniformly log-concave measure is globally Lipschitz. Note that the transfer of analytical properties does not depend on the optimality of the transport map. This is why several works have established Lipschitz bounds for other transport maps, such as those derived from diffusion processes, as introduced by Kim and Milman. Here, we use the control interpretation of the transport vector field inducing the transport map and a coupling strategy to obtain Lipschitz bounds for this map between asymptotically log-concave measures and their Lipschitz perturbations. This talk is based on a joint work with Giovanni Conforti.
========
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.

Seed Seminar of Mathematics and Physics
Fall’ 25 : Random Forests and Fermionic Field Theories
We show that a large class of fermionic theories are dual to a q → 0 limit of the Potts model in the presence of a magnetic field. These can be described using a statistical model of random forests on a graph, generalizing the (unrooted) random forest description of the Potts model with only nearest neighbor interactions. We then apply this to find a statistical description of a recently introduced family of  OSp(1|2M) invariant field theories that provide a UV completion to sigma models with the same symmetry.
The zoom link is available by subscribing to the mailing list: sympa@listes.math.cnrs.fr
========
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.

Seed Seminar of Mathematics and Physics
Fall’ 25: Random Forests and Fermionic Field Theories 
We consider the Renormalization Group (RG) fixed-point theory associated with a fermionic $psi^4_d$ model in d=1,2,3 with fractional kinetic term, whose scaling dimension is fixed so that the quartic interaction is weakly relevant in the RG sense. The model is defined in terms of a Grassmann functional integral with interaction $V^*$, solving a fixed-point RG equation in the presence of external fields, and a fixed ultraviolet cutoff. We define and construct the field and density scale-invariant response functions, and prove that the critical exponent of the former is the naive one, while that of the latter is anomalous and analytic. We construct the corresponding (almost-)scaling operators, whose two point correlations are scale-invariant up to a remainder term, which decays like a stretched exponential at distances larger than the inverse of the ultraviolet cutoff. Our proof is based on constructive RG methods and, specifically, on a convergent tree expansion for the generating function of correlations, which generalizes the approach developed by three of the authors in a previous publication (Giuliani et al. in JHEP 01:026, 2021. doi.org/10.1007/JHEP01(2021)026). CMP 406.10 (2025): 257, joint work with A. Giuliani, V. Mastropietro and S. Rychkov.
========
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.

Seed Seminar of Mathematics and Physics
Fall’ 25: Random Forests and Fermionic Field Theories 
The study of critical models is of the more active areas of statistical mechanics. Regarding the dimer model, the convergence of the critical model towards the Gaussian free field was obtained around 25 years ago by Kenyon. More recently, perturbations of the critical model known as near-critical models have been considered, and some convergence results have been obtained, in particular for the Ising model. Convergence results have also been obtained for the near-critical dimer model, which did not allow to identify the limiting field, even though it was conjectured to be the sine-Gordon field. I will present a derivation of the limit using discrete massive holomorphy techniques, which expresses the limiting field as the solution of a certain Dirichlet problem associated with a massive Dirac operator. I will finally explain how to relate this field to the sine-Gordon field. This is based on an ongoing work with Nathanaël Berestycki and Scott Mason.
========
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.

Seed Seminar of Mathematics and Physics
Fall’ 25: Random Forests and Fermionic Field Theories 
In two-dimensional models of critical non-intersecting loops, we conjecture an exact formula for three-point functions of fields that insert legs (open loop segments) and can have nonzero conformal spin. The conjecture extends a previous result for diagonal fields, recently proved by Ang-Cai-Sun-Wu, who also proved our conjecture for three spinless two-leg operators. We discuss in details the supporting evidence for our general conjecture coming from transfer-matrix computations using the unoriented Jones-Temperley-Lieb algebra.
========
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.

Seed Seminar of Mathematics and Physics
Fall’ 25: Random Forests and Fermionic Field Theories 
For many real-world networks, such as the World Wide Web, the degree distribution follows a power law. It is therefore useful to have simple random graph models whose limiting degree distribution exhibits this same feature. With this motivation, physicists Albert-László Barabási and Réka Albert introduced the preferential attachment model that now bears their name. A further advantage of this model is that it incorporates temporal dynamics: starting from an initial graph $mathcal{G}_0$, the graph at time $n+1$ is obtained from the graph at time $n$, denoted $mathcal{G}_n$, by adding a new vertex $v_{n+1}$. This vertex then attaches to one or several vertices of $mathcal{G}_n$ according to a preferential attachment rule, meaning that the probability of connecting to a given vertex of $mathcal{G}_n$ is proportional to its degree.
We present an extension of this model in which each vertex of the graph is assigned a community (or type), and in which the preferential attachment is sublinear; that is, the probability of attaching to a vertex $u$ is proportional to $deg(u)^gamma$, where $gamma$ is a parameter taking values in $(0,1)$.
========
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.

Seed Seminar of Mathematics and Physics
Fall’ 25 : Random Forests and Fermionic Field Theories  
The frozen Erdős-Rényi random graph is a variant of the standard dynamical Erdős-Rényi random graph that prevents the creation of the giant component by freezing the evolution of connected components with a unique cycle. The formation of multicyclic components is forbidden, and the growth of components with a unique cycle is slowed down, depending on a parameter p∈[0,1] that quantifies the slowdown. In this talk, we will study the fluid limit of the main statistics of this process, that is their functional convergence as the number of vertices of the graph becomes large and after a proper rescaling, to the solution of a system of differential equations. The proof is based on the free forest property of the frozen model: the forest part of the graph is a uniform random forest. In order to prove the fluid limit results, we will explain how to study and count forests using conditioned random walks.
========
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.

Seed Seminar of Mathematics and Physics
We consider FK models with $q$ in $[0,4]$ on the square lattice and the whole plane. We assume the convergence of height functions to GFF and in particular we assume that we know the variance $sigma^2$ of the GFF. Then, we sketch an approach to get the exponent $alpha_1$ describing the probability of having a primal crossing of an annulus. The basis for this approach is the BKW coupling relating the height function to the interface loops of FK. We show that by choosing appropriate test functions (viewd as placing charges on the plane), we can get relations between $sigma^2$, $alpha_1$, and a factor accounting for local concentration of small interface loops. 
 
========
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.

Running Seminar
We will introduce our themes and show some of the objects we will work on. The seminar will focus on the arithmetic and Hodge-theoretic aspects of differential equations, including accessory parameter problems, multiplication kernels, periods, character varieties, knot invariants, and related topics.
========
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.

Nonlinear dispersive equations are partial differential equations to describe various wave phenomena where the primary effects are wave dispersion and nonlinear interactions. Even a single equation can have many different types of solutions depending on the initial data, such as scattering, blow-up, and solitons.
The theme of this course is to classify global behavior of solutions in terms of the initial data. More precisely, the problem is to characterize the set of initial data corresponding to each type of solutions, together with the configuration of those sets, which also requires to analyze transient evolutions during intermediate time. Despite the recent progress for the soliton resolution conjecture, which classifies the asymptotic behavior, its link to the initial data is much less understood, mostly restricted in the data size, types of behavior, and by symmetry of the equation or the solutions.
The lecture will focus on two model cases as attempts to extend it in two directions. The first is to extend the initial data set to more variety of solutions; we consider the nonlinear Klein-Gordon equation and initial data near superposition of the ground state solitons, which are unstable. It is natural to expect that the classification is also a superposition of the single soliton case, but the interactions among unstable modes of different growth rates and large radiation from collapsed solitons can possibly spoil such a simple picture, by energy transfer from the most unstable mode to the others. I will show how to preclude it by using elementary geometry of the Lorentz transform and space-time weighted energy tailored for radiations from multi-solitons.
The second is to extend the equations to less symmetry; we consider the Zakharov system, which is a system of the Schrodinger and the wave equations with Hamiltonian and mass conservation, but without the Galilei or Lorentz invariance, nor the center of mass or energy. Such loss of structure poses serious difficulty especially in proving the rigidity that the minimal non-dispersive solutions must be the ground states. I will show how to overcome it, by combining virial-variational estimates and space-time estimates for non-radiative source terms.

Nonlinear dispersive equations are partial differential equations to describe various wave phenomena where the primary effects are wave dispersion and nonlinear interactions. Even a single equation can have many different types of solutions depending on the initial data, such as scattering, blow-up, and solitons.
The theme of this course is to classify global behavior of solutions in terms of the initial data. More precisely, the problem is to characterize the set of initial data corresponding to each type of solutions, together with the configuration of those sets, which also requires to analyze transient evolutions during intermediate time. Despite the recent progress for the soliton resolution conjecture, which classifies the asymptotic behavior, its link to the initial data is much less understood, mostly restricted in the data size, types of behavior, and by symmetry of the equation or the solutions.
The lecture will focus on two model cases as attempts to extend it in two directions. The first is to extend the initial data set to more variety of solutions; we consider the nonlinear Klein-Gordon equation and initial data near superposition of the ground state solitons, which are unstable. It is natural to expect that the classification is also a superposition of the single soliton case, but the interactions among unstable modes of different growth rates and large radiation from collapsed solitons can possibly spoil such a simple picture, by energy transfer from the most unstable mode to the others. I will show how to preclude it by using elementary geometry of the Lorentz transform and space-time weighted energy tailored for radiations from multi-solitons.
The second is to extend the equations to less symmetry; we consider the Zakharov system, which is a system of the Schrodinger and the wave equations with Hamiltonian and mass conservation, but without the Galilei or Lorentz invariance, nor the center of mass or energy. Such loss of structure poses serious difficulty especially in proving the rigidity that the minimal non-dispersive solutions must be the ground states. I will show how to overcome it, by combining virial-variational estimates and space-time estimates for non-radiative source terms.

Nonlinear dispersive equations are partial differential equations to describe various wave phenomena where the primary effects are wave dispersion and nonlinear interactions. Even a single equation can have many different types of solutions depending on the initial data, such as scattering, blow-up, and solitons.
The theme of this course is to classify global behavior of solutions in terms of the initial data. More precisely, the problem is to characterize the set of initial data corresponding to each type of solutions, together with the configuration of those sets, which also requires to analyze transient evolutions during intermediate time. Despite the recent progress for the soliton resolution conjecture, which classifies the asymptotic behavior, its link to the initial data is much less understood, mostly restricted in the data size, types of behavior, and by symmetry of the equation or the solutions.
The lecture will focus on two model cases as attempts to extend it in two directions. The first is to extend the initial data set to more variety of solutions; we consider the nonlinear Klein-Gordon equation and initial data near superposition of the ground state solitons, which are unstable. It is natural to expect that the classification is also a superposition of the single soliton case, but the interactions among unstable modes of different growth rates and large radiation from collapsed solitons can possibly spoil such a simple picture, by energy transfer from the most unstable mode to the others. I will show how to preclude it by using elementary geometry of the Lorentz transform and space-time weighted energy tailored for radiations from multi-solitons.
The second is to extend the equations to less symmetry; we consider the Zakharov system, which is a system of the Schrodinger and the wave equations with Hamiltonian and mass conservation, but without the Galilei or Lorentz invariance, nor the center of mass or energy. Such loss of structure poses serious difficulty especially in proving the rigidity that the minimal non-dispersive solutions must be the ground states. I will show how to overcome it, by combining virial-variational estimates and space-time estimates for non-radiative source terms.