Séminaire Analyse Harmonique
Integrable PDEs and interacting particle systems
02
June 2026
June 2026
| Intervenant : | Guilherme Silva |
| Institution : | Universidade de São Paulo |
| Heure : | 14h00 - 15h00 |
| Lieu : | Bâtiment 307, salle 2L8 |
We survey, from the perspective of a mathematical analyst, how statistics of interacting particle systems generate solutions to nonlinear integrable PDEs. In particular, we will talk about ongoing work on the Pearcey process—a universal point process arising as a scaling limit of non-intersecting random paths at cuspidal points. We discuss how this process generates solutions to the first members of the Boussinesq hierarchy, and explain how heuristics from the point process allow us to obtain rigorous scaling limits on the PDE side.
The talk is based on ongoing work with Mattia Cafasso (Université d'Angers), Thomas Chouteau (Universidade de São Paulo) and Alfredo Deaño (Universidad Carlos III Madrid).