Thu, 26 Mar 2026

15:00 - 17:00
L3

Renormalisation group on Lorentzian manifolds using (p)AQFT

Kasia Rejzner
(University of York)
Abstract

I will start the talk by discussing renormlisation group in perturbative algebraic quantum field theory (pAQFT) and its non-perturbative incarnation acting on the Buchholz-Fredenhagen dynamical C*-algebra. I will also explain how pAQFT can be used to derive functional renormlisation group (FRG) equations that generalize Wetterich equations to globally hyperbolic Lorentzian manifolds and arbitrary states (beyond the usual FRG in the vacuum).

Fri, 12 Jun 2026

11:00 - 12:00
L4

Scaling limits for a population model with growth, division and cross-diffusion

Dr Diane Peurichard
(INRIA Paris)
Abstract
Motivated by the modeling of bacteria microcolony morphogenesis across multiple scales, we explore in this talk models for a spatial population of interacting, growing and dividing particles. Starting from a microscopic stochastic model, we first write the corresponding stochastic differential equation satisfied by the empirical measure, and rigorously derive its mesoscopic (mean-field) limit. We then take an interest in the so-called localization limit, to reach a macroscopic (large-scale) model. The scaling consists in assuming that the range of interaction between individuals is very small compared to the size of the domain. In proving the localization limit using compactness arguments, the difficulties are twofold: first, growth and division render the system non-conservative, preventing the use of energy estimates. Second, the size of the particles, being a continuous trait, leads to new difficulties in obtaining compactness estimates. We first show rigorously the localization limit in the case without growth and fragmentation, under smoothness and symmetry assumptions for the interaction kernel. We then perform a thorough numerical study in order to compare the three modeling scales and study the different limits in situations not covered by the theory yet. These works provide a better understanding of the link between the micro- meso- and macro- scales for interacting particle systems. 
 
Co-authors: Marie Doumic (Ecole Polytechnique and Inria, CMA), Sophie Hecht (CNRS, Sorbonne Université) and Marc Hoffmann ( University Paris-Dauphine )
Fri, 01 May 2026

11:00 - 12:00
L4

Global stability and persistence for reaction systems and for generalized Lotka-Volterra systems 

Prof Gheorghe Craciun
(Dept of Mathematics University of Wisconsin-Madison)
Abstract

Reaction systems are continuos-time dynamical systems with polynomial right-hand side, and are very common in biochemistry, cell signaling, population dynamics, and many other biological applications. We discuss global stability (i.e., the existence of a globally attracting point) and persistence (i.e., robust absence of extinction) for large classes of reaction systems. In particular, we describe recent progress on the proof of the Global Attractor Conjecture (which says that vertex-balanced reaction systems are globally stable) and the Persistence Conjecture (which says that weakly-reversible reaction systems are persistent), and how these results can be extended outside their classical setting using the notion of “disguised reaction systems". We will also discuss analogous results for the case where reaction systems are replaced by generalized Lotka-Volterra systems of arbitrary degree. 

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