The SISSA seminar series "Probability, Statistical Mechanics and Quantum Fields" will be held during the trimester. See here for further information and Zoom access.
Invitation to Random Tensor Models: from random geometry to enumeration of tensor invariants
Reiko Toriumi (Okinawa Institute of Science and Technology)
Abstract: I will introduce random tensor models by first reviewing their motivation coming from random geometric approach to quantum gravity. I will also give some survey on the current topics around random tensors. Then, I will present recent results on enumeration of graphs representing tensor invariants based on arXiv:2404.16404[hep-th].
Time and location: Monday 5 October, 14:00-16:00, Room 133
Dynamics and spectrum in the semiclassical limit for non-self-adjoint operators
Alix Deleporte (Laboratoire de Mathématiques d'Orsay, Université Paris-Saclay)
Abstract: One of the early achievements of microlocal and semiclassical analysis was the asymptotic description, in a large frequency / small parameter case, of eigenvalues and (in the integrable case) eigenfunctions of self-adjoint operators. This is related to a refined description of the dynamics through the well-known Egorov theorem: quantum evolution is well-approximated by classical evolution. The non-self-adjoint case presents serious additional difficulties. Making sense of the appropriate "classical" objects, and proving the correspondence, necessitates a great deal of supplementary geometric and analytic work. In this talk, I will present the challenges associated with non-self-adjoint semiclassical analysis, and describe recent results as well as perspectives.
Time and location: Thursday 8 October, 14:00-16:00
A new approach to the hard-core Bose gas
Morris Brooks (University of Zürich)
Abstract: In this talk I will present a recent result on the ground-state energy of a Bosonic quantum gas with hard-core interactions (billiard balls), which proves the missing upper bound in the Lee-Huang-Yang formula. While this result settles a substantial open problem in the field, I want to put an emphasize on the genuinely novel methods used within. In the proof, we are naturally led to the study of a classical gas, whose probability distribution we characterize using the language of second quantization. In particular, I want to provide a perspective on the impact of our result beyond the boundaries of quantum mechanics.
Time and location: Thursday 15 October, 14:00-16:00
β-ensembles at intermediate temperature
Charlie Dworaczek Guera (KTH Stockholm)
Abstract: In this talk, I will present real β-ensembles of dimension N in the temperature regime 1/N<<β(N)<<1. In this regime, the system is still described macroscopically by the usual semicircle-type equilibrium measure. However, a transition occurs at mesoscopic scales: below a certain scale, the correlations are no longer strong enough, and the system enters a Poissonian regime. I will present a mesoscopic central limit theorem for linear statistics illustrating this transition, as well as the convergence of the local statistics to those of a Poisson point process. This is based on joint work with Gaultier Lambert, Michel Pain and Luke Peilen, and on the recent preprint arXiv:2609.25301.
Time and location: Thursday 22 October, 14:00-16:00