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.

The nonabelian Hodge correspondence provides a parametrization of the character variety of a surface group in a semisimple Lie group G by objects called Higgs bundles (which we will introduce). Among them, cyclic Higgs bundles stand out as candidates for representations with strong geometric properties. The Slodowy slice is a natural set of deformations of a Fuchsian representation in G, whose properties are yet to be described. In this talk, I will present some cases in which we are able to prove that representations in the cyclic Slodowy slice are Anosov, hence discrete and faithful, and correspond to some geometric structure that we describe. This is joint work with Colin Davalo and Qiongling Li.
 

We give an asymptotic formula for the number of common perpendiculars with length tending to infinity between two divergent geodesics in finite volume real hyperbolic manifolds, presenting a surprising non-purely exponential growth. We apply this result to count ambiguous geodesics in the modular curve, recovering results of Sarnak, and to prove a conjecture of Motohashi on the binary additive divisor problem in imaginary quadratic number fields. This is joint work with Jouni Parkkonen.
 

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
The Robinson–Trautman (RT) spacetime is an algebraically special solution of the vacuum Einstein equations. I will show that, in the absence of radiation, it corresponds to the vacuum sector of Euclidean Liouville theory. Moreover, upon linearization, the solution can be expressed as a superposition of specific quasi-normal modes of the Schwarzschild black hole. Finally, nonlinear effects—including memory—and the emergence of resonant modes in the radiation will also be discussed.
 
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.

In pure SU(n) 4D QCD, i.e. SU(n) Yang-Mills theory without matter, there exists stable long fluxtube strings which carry a 1-form symmetry charge. Over the past decade, there has been increasing evidence from lattice calculations that the worldsheet theories of such QCD strings contain a massive pseudoscalar (axion), at least when n>2. This has so far been puzzling from the perspective of holographic realizations of strings in confining gauge theories. In this talk, I will show how such axions appear naturally in the realization of 4D N=1 pure QCD from M-theory on non-compact G2 orbifolds. I will also show that this picture predicts that QCD string axions exist only if the gauge group is SU(n) (n>2), SO(4n+2), or E6 (or a quotient/double-cover thereof), and why I expect this pattern to hold for non-susy pure QCD as well. This pattern could be tested in future lattice studies of QCD strings for gauge groups of B, C, D, and E-type. 
 
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 Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Elucidating the nature of dark matter, dark energy, and dynamics of the early universe stand as major challenges of modern cosmology and particle physics. I will present a new program of addressing these challenges with spectroscopic galaxy surveys. This program builds on effective field theory (EFT) ideas borrowed from particle physics. The application of the EFT to large-scale structure allows for sub-percent precision analytic understanding of galaxy clustering on quasi-linear scales and provides an unmatched flexibility in testing new physics scenarios beyond the standard cosmological model. I will share some results of this program that include new measurements of fundamental cosmological parameters and novel constraints on dark energy, dark matter, and the physics of the early universe.
 
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.

This one-day workshop is organised jointly by Huawei and IHES, as a part of the IHES-Huawei partnership. The aim of the workshop is to bring together prominent voices from academia and industry to explore the evolving role of causal reasoning in artificial intelligence. The workshop will deliver meaningful dialogue around two major directions. The first one is theory-driven causal modelling, which focuses on theoretical approaches, frameworks, and tools for understanding causality, emphasizing the development of rigorous methods to identify, estimate, and interpret causal relationships. The second topic is machine learning with causal AI and its applications, which integrates machine learning and deep learning techniques to improve causal discovery, causal inference, causal representation learning and their corresponding application fields.
INVITED SPEAKERS: 

BOWDEN Jack (Exeter University, UK)
CADEI Riccardo (EPFL, Switzerland)
FUNG Pascale (HKUST & Visiting Professor at the Central Acad. of Fine Arts in Beijing)
HENCKEL Leonard (Univ. College, Dublin, UK)
LI Haoxuan (Peking University)
LIMNIOS Myrto (EPFL, Switzerland)
TIAN Jin (MBZUAI, Abu Dhabi)
ZHOU Hong (Huawei)

 
 

 
 
Organisers: Keshuang Li (Huawei), Keli ZHANG (Huawei)

We present a new structure on the first Galois cohomology of families of symplectic self-dual $p$-adic representations of $G_{Q_p}$ of rank two. This is a functorial decomposition into free rank one Lagrangian submodules encoding Bloch-Kato subgroups and epsilon factors, mirroring an underlying symplectic structure. This local sign decomposition has local as well as global applications, including compatibility of the Mazur-Rubin arithmetic local constants and epsilon factors, and new cases of the parity conjecture. It also leads to a formulation and proof of an analogue of Rubin’s conjecture over ramified quadratic extensions of $Q_p$, which initiates an integral Iwasawa theory for CM elliptic curves at primes of additive reduction. (Joint with A. Burungale, K. Nakamura, and K. Ota.)
 
========
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 purpose of this talk is to give fine limit theorems for the norm llgn…g1ll of a  product of random matrices, under some conditioning. These limit theorems are stated in analogy with the case of sums X1+…+Xn of real random variables. This is joint work with Ion Grama and Hui Xiao.