Matrix Models for Quantum Systems - Special Day of the Seed Seminar of Mathematics and Physics
vendredi 7 juin 2024 -
09:30
lundi 3 juin 2024
mardi 4 juin 2024
mercredi 5 juin 2024
jeudi 6 juin 2024
vendredi 7 juin 2024
09:30
Café d'accueil
Café d'accueil
09:30 - 10:00
Room: Centre de Conférences Marilyn et James Simons
10:00
Matrix Model for Structure Constants of "Huge" Protected Operators in N=4 SYM Theory
-
Vladimir Kazakov
(
Laboratoire de Physique de l'École Normale Supérieure, Paris
)
Matrix Model for Structure Constants of "Huge" Protected Operators in N=4 SYM Theory
Vladimir Kazakov
(
Laboratoire de Physique de l'École Normale Supérieure, Paris
)
10:00 - 11:00
Room: Centre de Conférences Marilyn et James Simons
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.
11:00
Pause Café
Pause Café
11:00 - 11:30
Room: Centre de Conférences Marilyn et James Simons
11:30
Entangleability of Cones
-
Guillaume Aubrun
(
Institut Camille Jordan, Lyon
)
Entangleability of Cones
Guillaume Aubrun
(
Institut Camille Jordan, Lyon
)
11:30 - 12:30
Room: Centre de Conférences Marilyn et James Simons
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)
12:30
Déjeuner-Buffet
Déjeuner-Buffet
12:30 - 14:00
Room: Centre de Conférences Marilyn et James Simons
14:00
Topological Recursion: a recursive way of counting surfaces
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Bertrand Eynard
(
Institut de Physique Théorique, CEA Saclay
)
Topological Recursion: a recursive way of counting surfaces
Bertrand Eynard
(
Institut de Physique Théorique, CEA Saclay
)
14:00 - 15:00
Room: Centre de Conférences Marilyn et James Simons
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.
15:00
Pause Café
Pause Café
15:00 - 15:30
Room: Centre de Conférences Marilyn et James Simons
15:30
Quantum Exclusion Process, Random Matrices and Free Cumulants
-
Philippe Biane
(
Laboratoire d'Informatique Gaspard Monge, Marne-la-Vallée
)
Quantum Exclusion Process, Random Matrices and Free Cumulants
Philippe Biane
(
Laboratoire d'Informatique Gaspard Monge, Marne-la-Vallée
)
15:30 - 16:30
Room: Centre de Conférences Marilyn et James Simons
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.