Matrix Models for Quantum Systems - Special Day of the Seed Seminar of Mathematics and Physics

vendredi 7 juin 2024, 09:30 → 16:30 Europe/Paris

Centre de Conférences Marilyn et James Simons (Le Bois-Marie)

The Seed seminar of mathematics and physics is a seminar series that aims to foster interactions between mathematicians and theoretical physicists, with both online and in-person events. It is holding a special day on Matrix models for quantum systems at IHES, with contributions from Guillaume Aubrun, Philippe Biane, Bertrand Eynard and Vladimir Kazakov.

 

Registration is free and open until May 31, 2024.

Invited speakers:
Guillaume Aubrun (Institut Camille Jordan, Lyon)
Philippe Biane (Laboratoire d'Informatique Gaspard Monge, Marne-la-Vallée)
Bertrand Eynard (Institut de Physique Théorique, CEA Saclay)
Vladimir Kazakov (Laboratoire de Physique de l'École Normale Supérieure, Paris)

Scientific Committee: 
Thierry Bodineau ( IHES)
Slava Rychkov (IHES)

Organizing Committee: 
Ariane Carrance (CMAP)
Matteo D'Achille (LMO)
Edoardo Lauria (LPENS)

Poster June 2024 IHES event.pdf

09:30 Café d'accueil

1 Matrix Model for Structure Constants of "Huge" Protected Operators in N=4 SYM Theory

Huge operators in N = 4 SYM theory correspond to sources so heavy that they fully backreact on the space-time geometry. Here we study the protected correlation function of three such huge operators when they are given by 1/2 BPS operators , dual to IIB Strings in AdS5 × S 5 . We unveil simple matrix model representations for these correlators which we can sometimes solve analytically. For general huge operators, we transform this matrix model into a 1 + 1 dimensional integrable hydrodynamics problem. A discrete counterpart of this system -– the rational Calogero-Moser Model - helps to numerically solve the problem for general huge operators.

Orateur: Vladimir Kazakov (Laboratoire de Physique de l'École Normale Supérieure, Paris)

Vidéo

11:00 Pause Café

2 Entangleability of Cones

We solve a long-standing conjecture by Barker, proving that the minimal and maximal tensor products of two finite-dimensional proper cones coincide if and only if one of the two cones is generated by a linearly independent set. Here, given two proper cones $C1, C2$, their minimal tensor product is the cone generated by products of the form $x1 \otimes x2$, where $x1 \in C1$ and $x2 \in C2$, while their maximal tensor product is the set of tensors that are positive under all product functionals $f1 \otimes f2$, where $f1$ is positive on $C1$ and $f2$ is positive on $C2$. Our proof techniques involve a mix of convex geometry, elementary algebraic topology, and computations inspired by quantum information theory. Our motivation comes from the foundations of physics: as an application, we show that any two non-classical systems modelled by general probabilistic theories can be entangled.
(Joint work with Ludovico Lami, Carlos Palazuelos, Martin Plavala)

Orateur: Guillaume Aubrun (Institut Camille Jordan, Lyon)

Vidéo

12:30 Déjeuner-Buffet

3 Topological Recursion: a recursive way of counting surfaces

Enumerating various kinds of surfaces is an important goal in combinatorics of maps, enumerative geometry, string theory, statistical physics, and other areas of mathematics or theoretical physics. For example the famous Mirzakhani's recursion is about enumerating hyperbolic surfaces. It is often easier to enumerate planar surfaces, with the lowest topologies (disc, cylinder), and the question is how to enumerate surfaces of higher genus and with more boundaries. Many of the surface enumeration problems, satisfy a universal recursion, known as the "topological recursion", which, from the enumeration of discs and cylinders, gives all the other topologies. Moreover this recursion has many beautiful mathematical properties by itself, and allows to make the link with other areas of mathematics and physics, in particular integrable systems, random matrices, and many others.

Orateur: Bertrand Eynard (Institut de Physique Théorique, CEA Saclay)

Vidéo

15:00 Pause Café

4 Quantum Exclusion Process, Random Matrices and Free Cumulants

The Quantum Symmetric Simple Exclusion Process (QSSEP) is a model of quantum particles hopping on a finite interval and satisfying the exclusion principle. I will explain how free cumulants, which are quantities arising in free probability and random matrix theory, encode the fluctuations of the invariant measure of this process when the number of sites goes to infinity.

Orateur: Philippe Biane (Laboratoire d'Informatique Gaspard Monge, Marne-la-Vallée)

Vidéo