Probability and Mathematical Physics Seminar

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Probability and the City Seminar

Speaker: Christophe Garban (Courant & Université Lyon 1) and Jérémie Bouttier (Sorbonne / IMJ-PRG)

Location: Warren Weaver Hall 1302

Date: Friday, April 17, 2026, 11:10 a.m.

Synopsis:

Christophe Garban (Courant & Université Lyon 1), 11:10 AM

Small perturbations of the classical Heisenberg model

While there is a deep mathematical understanding of the 2D Ising model, its continuous $S^2$-valued counterpart—the classical Heisenberg model—remains one of the most significant challenges in mathematical physics. In 1975, Polyakov predicted that this system remains highly decorrelated at all positive temperatures due to its non-abelian symmetry. In this talk, I will discuss the behavior of this model under small perturbations of the sphere's geometry. I will highlight how this problem naturally connects to questions in analysis, such as the properties of harmonic maps. No prior background in spin systems will be assumed. This is a joint work with Nathan de Montgolfier.

 

Jérémie Bouttier (Sorbonne / IMJ-PRG), 12:10 PM

The slice decomposition of planar maps

Random planar maps, also known as dynamical tesselations, are simple yet rich models of 2D random geometries. Over the last decades, their understanding has been greatly improved by combinatorial methods. In this talk I will present such a method, the slice decomposition, which consists in cutting surfaces along geodesics. Based on joint works with Emmanuel Guitter, Marie Albenque, Grégory Miermont, Hugo Manet, Thomas Lejeune and Bertrand Eynard (in chronological order).

 

Speakers' websites

Christophe: https://math.univ-lyon1.fr/~garban/

Jérémie: https://perso.imj-prg.fr/jeremie-bouttier/home/