Séminaire : Problèmes Spectraux en Physique Mathématique
Le séminaire a lieu un lundi par mois à l'Institut Henri Poincaré en Salle Pierre Grisvard (3ème étage). La journée commence par un café à 10h30 dans l'espace Emile Borel au 2ème étage.
Venir à l'IHP | Institut Henri Poincaré
Pour toute question ou suggestion pour le séminaire, vous pouvez vous adresser à Yannick Guedes Bonthonneau, Constanza Rojas-Molina ou Clément Tauber.
Prochain Séminaire : lundi 12 octobre 2026
- 11h-12h : Yannick Guedes Bonthonneau (DMA, ENS)
- 14h-15h : Nguyen Viet Dang (IRMA, Université de Strasbourg)
Yang-Mills measure in 2 dimensions and its semiclassical limit
Abstract: Gauge theory, which goes back to Maxwell, is a central topic in physics and mathematics. In this talk, I will survey recent works with Bonthonneau-Chhaibi-Rivière-To and with Nohra on Yang--Mills theory in 2 dimensions from the point of view of dynamical systems and probability. I will explain how we construct a Yang-Mills measure on the space of distributional connections on a surface and in what sense this measure converges to the Atiyah-Bott-Goldman symplectic volume when the surface area goes to zero.
- 15h20-16h20 : Sarah Timhadjelt (Institut Fourier, Université Grenoble Alpes)
Quantum channel expanders obtained with Haar distributed unitaries
Abstract: We study the expansion (or spectral gap) of a non-Hermitian quantum channel obtained by summing tensor products of independent Haar-distributed unitaries. By following Hastings' method to upper-bound the spectral gap in terms of eigenvalues for the Hermitian case, and adapting it we will provide an exact estimate of the spectral gap in terms of singular values. We therefore we obtain a random quantum expander in terms of both singular values and eigenvalues for the non-Hermitian case. We also provide a deterministic lower bound for the second largest singular value, analogous to the Alon-Boppana bound for d-regular graphs. The upper bound is obtained using Schwinger-Dyson equations.
Dates des séminaires 2026-2027
- 12 octobre 2026
- 16 novembre 2026
- 14 décembre 2026
- 11 janvier 2027
- 22 février 2027
- 15 mars 2027
- 19 avril 2027
- 10 mai 2027
- 14 juin 2027