Thu, 23 Oct 2025
14:00
L4

Multifold Schwinger-Keldysh EFT -- what I understand and what I don't

Akash Jain
Abstract

The organisers asked me to give a brief talk on what I’ve been thinking about lately. So, I’ll tell you about Schwinger-Keldysh EFTs: an EFT framework for non-equilibrium dissipative systems such as hydrodynamics. These are built on a closed-time contour that runs forward and backward in time, allowing access to a variety of non-equilibrium observables. However, these EFTs fundamentally miss a wider class of observables, called out-of-time-ordered correlators (OTOCs), which are closely tied to quantum chaos. In this talk, I’ll share some thoughts on extending Schwinger-Keldysh EFTs to multifold contours that capture such observables. I’ll also touch on the discrete KMS symmetry of thermal systems, which generalises from Z_2 in the single-fold case to the dihedral group in the -fold case. With any luck, I’ll reach the point where I’m stuck and you can help me figure it out.

Tue, 21 Oct 2025

14:00 - 15:00
L4

Algebraic relations for permutons

Omer Angel
(University of British Columbia)
Abstract

Permutons are a framework set up for understanding large permutations, and are instrumental in pattern densities. However, they miss most of the algebraic properties of permutations. I will discuss what can still be said in this direction, and some possible ways to move beyond permutons. Joint with Fiona Skerman and Peter Winkler.

Tue, 14 Oct 2025

14:00 - 15:00
L4

An exponential upper bound on induced Ramsey numbers

Marcelo Campos
(Instituto Nacional de Matemática Pura e Aplicada (IMPA))
Abstract
The induced Ramsey number $R_{ind}(H)$ of a graph $H$ is the minimum number $N$ such that there exists a graph with $N$ vertices for which all red/blue colorings of its edges contain a monochromatic induced copy of $H$. In this talk I'll show there exists an absolute constant $C > 0$ such that, for every graph $H$ on $k$ vertices, these numbers satisfy $R_{ind}(H) ≤ 2^{Ck}$. This resolves a conjecture of Erdős from 1975.
 
This is joint work with Lucas Aragão, Gabriel Dahia, Rafael Filipe and João Marciano.
Mon, 17 Nov 2025

16:30 - 17:30
L4

Existence and nonexistence for equations of fluctuating hydrodynamics

Prof Johannes Zimmer
( TU-Munich)
Abstract

Equations of fluctuating hydrodynamics, also called Dean-Kawasaki type equations, are stochastic PDEs describing the evolution of finitely many interacting particles which obey a Langevin equation. First, we give a mathematical derivation for such equations. The focus is on systems of interacting particles described by second order Langevin equations. For such systems,  the equations of fluctuating hydrodynamics are a stochastic variant of Vlasov-Fokker-Planck equations, where the noise is white in space and time, conservative and multiplicative. We show a dichotomy previously known for purely diffusive systems holds here as well: Solutions exist only for suitable atomic initial data, but provably not for any other initial data. The class of systems covered includes several models of active matter. We will also discuss regularisations, where existence results hold under weaker assumptions. 

Mon, 27 Oct 2025

16:30 - 17:30
L4

Spatially-extended mean-field PDEs as universal limits of large, heterogeneous networks of spiking neurons

Dr Valentin Schmutz
(University College London)
Abstract

The dynamics of spatially-structured networks of N interacting stochastic neurons can be described by deterministic population equations in the mean-field limit. While this is known, a general question has remained unanswered: does synaptic weight scaling suffice, by itself, to guarantee the convergence of network dynamics to a deterministic population equation, even when networks are not assumed to be homogeneous or spatially structured? In this work, we consider networks of stochastic integrate-and-fire neurons with arbitrary synaptic weights satisfying a O(1/N) scaling condition. Borrowing results from the theory of dense graph limits, or graphons, we prove that, as N tends to infinity, and up to the extraction of a subsequence, the empirical measure of the neurons' membrane potentials converges to the solution of a spatially-extended mean-field partial differential equation (PDE). Our proof requires analytical techniques that go beyond standard propagation of chaos methods. In particular, we introduce a weak metric that depends on the dense graph limit kernel and we show how the weak convergence of the initial data can be obtained by propagating the regularity of the limit kernel along the dual-backward equation associated with the spatially-extended mean-field PDE. Overall, this result invites us to reinterpret spatially-extended population equations as universal mean-field limits of networks of neurons with O(1/N) synaptic weight scaling. This work was done in collaboration with Pierre-Emmanuel Jabin (Penn State) and Datong Zhou (Sorbonne Université).

Tue, 28 Oct 2025
15:30
L4

TBA

Jakob Stein
(State University of Campinas and University of Oxford)
Subscribe to L4