Mon, 02 Feb 2026

16:30 - 17:30
L4

Mean-field limits of non-exchangeable interacting diffusions on co-evolutionary networks

Prof. David Poyato
(University of Granada)
Abstract
Multi-agent systems are ubiquitous in Science, and they can be regarded as large systems of interacting particles with the ability to generate large-scale self-organized structures from simple local interactions rules between each agent and its neighbors. Since the size of the system is typically huge, an important question is to connect the microscopic and macroscopic scales in terms of mean-field limits, which is a fundamental problem in Physics and Mathematics closely related to Hilbert Sixth Problem. In most real-life applications, the communication between agents is not based on uniform all-to-all couplings, but on highly heterogeneous connections, and this makes agents distinguishable. However, the classical strategies based on mean-field limits are strongly based on the crucial assumption that agents are indistinguishable, and it therefore does not apply to our distinguishable setting, so that we need substantially new ideas.
 
In this talk I will present a recent work about the rigorous derivation of the mean-field limit for systems of non-exchangeable interacting diffusions on co-evolutionary networks. While previous research has primarily addressed continuum limits or systems with linear weight dynamics, our work overcomes these restrictions. The main challenge arises from the coupling between the network weight dynamics and the agents' states, which results in a non-Markovian dynamics where the system’s future depends on its entire history. Consequently, the mean-field limit is not described by a partial differential equation, but by a system of non-Markovian stochastic integrodifferential equations. A second difficulty stems from the non-linear weight dynamics, which requires a careful choice for the limiting network structure. Due to the limitations of the classical theory of graphons (Lovász and Szegedy, 2006) in handling non-linearities, we employ K-graphons (Lovász and Szegedy, 2010), also termed probability-graphons (Abraham, Delmas, and Weibel, 2025). This framework pro seems to provide a natural topology that is compatible with such non-linearities.
 
This is a joint work with Julián Cabrera-Nyst (University of Granada).
Thu, 30 Oct 2025

12:00 - 13:00
C5

Differentiation on metric spaces

Pietro Wald
(University of Warwick)
Abstract
Cheeger’s seminal 1999 paper initiated the study of metric measure spaces that admit a generalised differentiable structure. In such spaces, Lipschitz functions—real-valued and, in some cases, Banach-valued—are differentiable almost everywhere. Since then, much work has gone into determining the precise geometric and analytic conditions under which such structures exist. In this talk, I will give a brief overview of the theory and present new results from joint work with David Bate.
Wed, 12 Nov 2025

11:00 - 13:00
L4

2d Sinh-Gordon model on the infinite cylinder

Trishen Gunaratnam
(Tata Institute for Fundamental Research)
Abstract

The 2d (massless) Sinh-Gordon model is amongst the simplest 2d quantum field theories that are expected to be integrable (= infinitely many symmetries), but without conformal symmetry. In this talk I will explain a rigorous construction of this model and its vertex correlations (= Laplace transforms) on the infinite cylinder using probability theory. A fundamental role is played by the Sinh-Gordon Hamiltonian and I will explain how the theory of Gaussian multiplicative chaos can be used to analyze this linear map. This talk will be based on joint work with Colin Guillarmou and Vincent Vargas.

Wed, 05 Nov 2025
11:00
L4

Coming up from $-\infty$ for KPZ via stochastic control

Carlos Villanueva Mariz
(Free University Berlin)
Abstract

We derive a lower bound, independent of the initial condition, for the solution of the KPZ equation on the torus, using its representation as the value function of a stochastic control problem.

With the same techniques we also prove a bound for its oscillation, again independent of initial conditions, which is related to Harnack's inequality for the (rough) heat equation.

 

Wed, 03 Dec 2025
11:00
L4

What future for mathematics?

Ivan Nourdin
(University of Luxembourg)
Abstract

In this talk, we will explore the emerging role of generative AI in mathematical research. Building on insights from the “Malliavin–Stein experiment”, carried out in collaboration with Charles-Philippe Diez and Luis Da Maia, we will discuss our experience and reflect on how AI might influence the way mathematics is conceived, proven, and created.

Tue, 04 Nov 2025
13:45
L3

Lean tutorial (part 2)

Remy Degenne
(INRIA LILLE)
Abstract

This tutorial will be a hands-on introduction to proving theorems in Lean, using its mathematical library Mathlib. It will not assume any previous knowledge about formal theorem provers. We will discover the Lean language, learn how to read a statement and a proof, and learn the essential "tactics" one can use to prove theorems in Lean.

Participants should come with a computer, and it would be best if they could install Lean before the tutorial by following the instructions at https://lean-lang.org/install/ . The installation should be easy and takes only a few minutes.

Tue, 04 Nov 2025
12:00
L4

Lean tutorial (part 1)

Remy Degenne
(INRIA LILLE)
Abstract
This tutorial will be a hands-on introduction to proving theorems in Lean, using its mathematical library Mathlib. It will not assume any previous knowledge about formal theorem provers. We will discover the Lean language, learn how to read a statement and a proof, and learn the essential "tactics" one can use to prove theorems in Lean.
Participants should come with a computer, and it would be best if they could install Lean before the tutorial by following the instructions at https://lean-lang.org/install/ . The installation should be easy and takes only a few minutes.
Tue, 25 Nov 2025

14:00 - 15:00
L4

Poset Saturation - From the Diamond to the General Case

Maria-Romina Ivan
(University of Cambridge, Stanford University)
Abstract

Given a finite poset $P$ we ask how small a family of subsets of $[n]$ can be such that it does not contain an induced copy of the poset, but adding any other subset creates such a copy. This number is called the saturation number of $P$, denoted by $\operatorname{sat}^*(n,P)$. Despite the apparent similarity to the saturation for graphs, this notion is vastly different. For example, it has been shown that the saturation numbers exhibit a dichotomy: for any poset, the saturation number is either bounded, or at least $2 n^{1/2}$. In fact, it is believed that the saturation number is always bounded or exactly linear. In this talk we will be discussing the most recent advances in this field, with the focus on the diamond poset, whose saturation number was unknown until recently.

Joint with Sean Jaffe.

Fri, 24 Oct 2025
11:00
L3

Higher-Form Anomalies on Lattice

Ryohei Kobayashi
(IAS Princeton)
Abstract
Higher-form symmetry in a tensor product Hilbert space is always emergent: the symmetry generators become genuinely topological only when the Gauss law is energetically enforced at low energies. In this talk, I explain a general method for defining the 't Hooft anomaly of higher-form symmetries in lattice models built on a tensor product Hilbert space. For instance, this allows us to define an index valued in $H^4(B^2G, U(1))$ characterizing the ’t Hooft anomaly of 1-form symmetry (2+1)D, for given finite depth circuits generating the symmetry. I also outline a criteria for “onsiteability” of higher-form symmetry based on an ongoing work with collaborators.


 

Subscribe to