Charles Marteau (groupe Théorie des cordes)

Boundary structures and holographic fluids in gravity

Abstract

This thesis is devoted to the study of several aspects of dynamical spacetimes with boundaries. An emphasis is put on asymptotic boundaries such as the conformal boundary of AdS or the null infinity in flat space. In AdS the geometry of the conformal boundary is pseudo-Riemannian since the boundary is time-like. In flat space, we will show how the geometry of the null infinity can be described in terms of Carroll structure. The latter emerges as the ultra-relativistic limit, or c → 0 limit, of a pseudo-Riemannian geometry. In particular, the flat limit in the bulk maps to this ultra-relativistic limit on the boundary. We will also see how the symmetries of asymptotically flat gravity translate into global symmetries of this exotic boundary geometry. This analysis is of central importance in fluid/gravity correspondence since the fluid is expected to live on the boundary. In this context we find integrability conditions on the boundary fluid that allow for a resummation of the so-called Derivative Expansion in AdS. The flat limit gives rise to the notion of Carrollian fluid on the boundary whose hydrodynamical expansion maps to a flat version of the Derivative expansion in the bulk, thus providing a notion of fluid/gravity correspondence in flat space. A second type of boundary that we study is the one formed by the horizon of a black hole. There, another type of fluid/gravity correspondence exists: the membrane paradigm. We revisit this concept and propose a novel interpretation of the Damour–Navier–Stokes equation in terms of ultra-relativistic conservation laws.

Jury

Dionysios ANNINOS, Kings College, Londres
Glenn BARNICH, Université Libre de Bruxelles
Daniel GRUMILLER, TU Wien, Vienne
Niels OBERS, Niels Bohr Institute, Copenhague et Nordita, Stockholm
Marios PETROPOULOS, École Polytechnique, IP Paris (directeur de thèse)
Andrea PUHM, École Polytechnique, IP Paris

Organisation

La soutenance aura lieu par conférence zoom le vendredi 19 juin 2020 à 10h30. L’accueil sera assuré dès 10h. Les retardataires ne seront pas admis en salle virtuelle avant l’entracte.

Les coordonnées de la connexion peuvent être obtenues sur demande auprès de Malika Lang, Charles Marteau ou Marios Petropoulos.

Annulé

Frank Redig will give six lectures, grouped into three sessions, at the following dates : 19 May, 26 May, 2 June, from 10:30 to 12:30, in the conference room Louis Michel.

The lectures will be centred around the theory and applications of duality in the context of interacting particle systems and non-equilibrium statistical physics models. Duality is a powerful tool in Markov process theory, allowing to connect two processes (the process under study and its dual) via a so-called duality function. Often the dual process is simpler, e.g., in systems coupled with reservoirs in  the dual the reservoirs are replaced by absorbing boundaries, or in infinite interacting systems, the dual is a system of finitely many particles, or in the context of diffusion processes, the dual is a simple discrete jump process.
We show how to understand dualities from the point of view of an underlying Lie algebra of symmetries (operators commuting with the generator).
This approach gives several new dualities, and new duality functions, such as orthogonal duality functions. It also allows to constructively define processes with dualities, and to find ``correct’’ asymmetric versions of symmetric models with dualities (via so-called q-deformation).
We will explain this theory starting from simple examples (such as independent random walkers, exclusion process, inclusion process), and provide several applications in the description of non-equilibrium steady states as well as in hydrodynamic limits and fluctuation fields.

Lecture 1: Introduction, motivation, some background from Markov process theory

Lecture 2: Duality: definition, duality and symmetries, duality and intertwining, duality and change of representation. Examples.

Lecture 3: Dualities for independent random walkers: self-duality, duality with deterministic system, averaging models. Applications to hydrodynamic limits and fluctuation fields and to ergodic theory.

Lectures 4-5: The symmetric inclusion process (SIP) and its dual processes: Lie algebraic construction via co-product of the Casimir.
Discrete and continuous representations, diffusion processes dual to SIP. Thermalization, models of KMP type, inhomogeneous systems.

Lecture 6: Non-equilibrium steady states: duality with reservoirs. Consistency, orthogonal polynomial duality. Universal properties of correlation functions of non-equilibrium steady states.

Séminaire annulé

Salle de conférence  Louis Michel

Speaker: Grégory Schehr, LPTMS 

Title: Large deviations of the top eigenvalue of random matrices and applications in statistical physics

Abstract: The statistical properties of the largest eigenvalue of a random matrix are of interest in diverse fields such as in the stability of large ecosystems, in disordered systems and related stochastic growth processes, in statistical data analysis and even in string theory. In this talk I will discuss the developments in the theory of extremely rare fluctuations (large deviations) of the largest eigenvalue using a Coulomb gas approach. I will discuss in particular the third-order phase transition which separates the left tail from the right tail, a transition akin to the so-called Gross-Witten-Wadia phase transition found in 2-d lattice quantum chromodynamics.

Salle de Conférence Louis Michel

14:00-15:00 : Bart van Ginkel

Title: Hydrodynamic limit of the Symmetric Exclusion Process on compact Riemannian manifolds.

Abstract: In this talk I will first explain the concept of the hydrodynamic limit of an interacting particle system. The idea is that one wants to show that when both space and time are rescaled (appropriately), the limiting densities of particles satisfy some PDE. This will be illustrated with the Symmetric Exclusion Process. Then we move this basic particle system to a hard context: Riemannian manifolds. I will highlight which challenges arise in the curved setting and how we deal with them. Joint work with Frank Redig.

15:00-16:00 : Rik Versendaal

Title: Large deviations for geodesic random walks.

Abstract: The theory of large deviations is concerned with the limiting behaviour on the exponential scale of a sequence of random variables. A fundamental result is Cramér’s theorem, which states that the empirical mean of a sequence of i.i.d. random variables satisfies a so called large deviations principle. Mogulskii’s theorem is concerned with the corresponding path space large deviations. To study the analogue of these theorems for a Riemannian manifold, we introduce a generalization of random walks to a manifold, called geodesic random walks. We present the analogues of Cramér’s and Mogulskii’s theorem for geodesic random walks and write down the rate function for these large deviations principles.

Une première édition digitale aura lieu le  MARDI 16 JUIN DE 14H A 16H30

Découvrez le programme et inscrivez-vous ici

Organisée par des chercheurs pour les chercheurs et les doctorants, l’objectif de cette journée conviviale est de réunir les dix communautés de l’Institut afin d’offrir un panorama de le recherche réalisée au sein de ses laboratoires. Au programme : des présentations dynamiques de 5 minutes sur des thématiques variées montrant la richesse des recherches de nos laboratoires, des discours scientifiques croisés faisant le lien entre des sujets de plusieurs disciplines, des échanges autours de posters scientifiques, etc. Plus de détails seront bientôt communiqués.

Comité d’organisation : Isabelle Bloch (Telecom Paris), Jean-René Chazottes (École polytechnique), Arnak Dalalyan (Ensae), Maryline Laurent (Telecom SudParis), Jean-François Semblat (Ensta Paris), avec l’aide de Chloé Aubisse et Solange Ricard (direction de la communication de l'École polytechnique).

Une édition en présentiel aura lieu à une date qui reste à définir en fonction de l'évolution des conditions sanitaires.

CPHT, Ecole Polytechnique, Salle de Conférence Louis Michel

Ariane Carrance (Laboratoire de Mathématiques d'Orsay, Université Paris Sud) 

Title: La carte brownienne, un modèle de gravité quantique 2D de plus en plus universel

Abstract: La question fondamentale de l'unification de la mécanique quantique et de la relativité générale en une théorie cohérente de la gravité quantique peut se traduire en divers problèmes concrets plus ou moins ambitieux. Ainsi, une approche possible est de chercher à définir un espace métrique aléatoire (et non quantique), continu, qui puisse être interprété comme un espace-temps aléatoire. Une manière plus spécifique d'obtenir un tel espace-temps est de le construire comme limite d'échelle d'espaces métriques discrets. En dimension 2, c'est ainsi que la carte brownienne s'obtient comme limite d'échelle de nombreuses familles de cartes planaires. Après avoir introduit les notions nécessaires pour comprendre ces limites, je présenterai un résultat qui étend la classe d'universalité des modèles discrets qui convergent vers la carte brownienne, et la relie plus explicitement à des modèles reposant sur le calcul de Regge, tels que les Triangulations Dynamiques, ainsi qu'au cas 2D des modèles de tenseurs colorés.

CPHT, Ecole Polytechnique, Salle de Conférence Louis Michel

Giuseppe Policastro (ENS)

Title: Quantum complexity and holography

Abstract: I will discuss the motivations for introducing the notion of quantum complexity in physics, coming from the issues related to the information loss paradox in black holes. I will introduce the definition of complexity, the different proposals for its holographic computation, its inherent ambiguity, then present the computation for the case of a boundary/defect CFT.

Ridge, NY, 26 February 2020 — The American Physical Society (APS) has selected 147 Outstanding Referees for 2020 that have demonstrated exceptional work in the assessment of manuscripts published in the Physical Review journals. A full list of the Outstanding Referees is available online at http://journals.aps.org/OutstandingReferees.

The Summer School will take place from July 7 to July 17 2020 at the Institut d'Etudes Scientifiques de Cargèse, located on the west cost of the beautiful Corsica island, nearby the city of Ajaccio.

The purpose of this Summer School is to train the next generation of young researchers in the field of quantum simulation and, more generally, quantum technologies. Grouping together a diverse community as well as young and leading senior researchers, we expect a stimulating cross-fertilization of ideas, methods, and approaches, able to further develop this fields beyond the present frontiers.

Information about the Summer School, including a list of speakers and application forms can be found on the website: 
https://quantsim2020.sciencesconf.org

Important dates
Opening of applications: Mon, 24 Feb 2020
Deadline for application: Fri, 20 March 2020
Notification of acceptance: Mid-April
Deadline for registration: Mon, 15 May 2020

Organizers 
Thierry Giamarchi, Giacomo Roati, and Laurent Sanchez-Palencia

Silke Biermann, Présidente du Département de Physique à l'Ecole Polytechnique, Professeur à l'Ecole Polytechnique et chercheuse au Centre de Physique Théorique, s'est vue décerner la médaille d'argent du CNRS pour ses travaux développant des approches de calculs de structures électroniques pour les matériaux corrélés à partir de premiers principes.

La médaille d'argent distingue des chercheurs et des chercheuses pour l'originalité, la qualité et l'importance de leurs travaux, reconnus sur le plan national et international.