The construction of braneworlds localizing massless gravity on subsurfaces of spacetimes with infinite transverse spaces has remained an open problem. There have even been some "no-go" theorems claiming to show that such constructions are not possible. The talk will present a resolution of this problem simply based upon a hyperbolic solution of type IIA theory with a superposed Neveu-Schwarz 5-brane. Gravity is bound to the brane surface owing to the existence of a single normalizable bound state of the transverse space Laplacian.

The black hole firewall problem is a conflict between three important physical principles: causality, unitarity, and the equivalence principle. I will describe how the conflict arises in the description of Hawking radiation from a black hole, and explain why resolving the problem is crucially important for our understanding of quantum gravity. I will briefly describe possible resolutions of the conflict. Solving the firewall problem is likely to teach us something important about quantum gravity.

Dans ce cours nous étudierons plusieurs modèles de graphes aléatoires allant du plus classique (le modèle d'Erdös-Renyi introduit en 1960) aux plus récents (les cartes planaires aléatoires étudiées depuis le début des années 2000). Le fil conducteur du cours sera la notion de convergence locale et les propriétés des graphes limites dits dilués.

Contenu du cours :

– Modèle d'Erdös-Renyi, transition de phase et propriétés de base
– Convergence locale et "méthode objective" d'Aldous et Steele
– Arbre couvrant minimum et théorème de Frieze 
– Graphes aléatoires unimodulaires
– Limites locales d'arbres aléatoires
– Limites locales de cartes aléatoires (construction, épluchage, théorème de Benjamini-Schramm)

The goal of this talk is to give a pedagogical introduction to Bell’s theorem and its implication for our view of the physical world, in particular how it establishes the existence of non-local effects or of actions at a distance. We also discuss several misunderstandings of Bell’s result and we will explain how the de Broglie-Bohm theory allows us to understand, to some extent, what non-locality is.

Dans cet exposé, je présenterai certains résultats mathématiques  récents concernant la limite de champ moyen pour des systèmes quantiques en  interaction, le lien avec la condensation de Bose-Einstein et la théorie de  Bogoliubov.

In this talk I will advocate the need to explore the properties of Fermi statistics. Although most investigations have been done with electrons in quantum conductors, the effects presented here are relevant for any fermionic systems.
In phase coherent conductors electrons behave as effective non interacting Fermions (Landau quasiparticles). Reducing the lateral size of ultra-clean conductors to achieve perfect control of the electron transmission has enable experiments revealing fundamental and sometime unexpected properties of the Fermi sea: conductance quantization, noiseless current, electron anti-bunching, continuous single electron injection from a voltage biased a contact, spontaneous creation of spin entangled electron-hole pairs in tunnel barrier, to cite a few.
Further Fermi statistics entanglement properties can be investigated in a linear electron optics scheme, mimicking quantum optics with electrons replacing photons. This requires realizing single electron sources, a challenging issue as contrary to photons, which propagate in vacuum, single electrons must be launched on top of a Fermi sea prone to generate extra excitations. However a magic combination of Fermi statistics and wave properties allow time-resolved single electron to be created in the form of minimal excitation states called Leviton. Single electron sources, either time or energy resolved, have been recently used in single electron partitioning experiments and to measure two-(or more) electron Hong Ou Mandel correlations. If time permits some possible extensions to anyonic quasi-particles like the Laughlin quasi-particles of the Quantum Hall Effect will be discussed.

In my talk I will discuss a family of matrix models, which describes the generating functions of intersection numbers on moduli spaces both for open and closed Riemann surfaces. Linear (VirasoroW-constraints) and bilinear (KPMKP integrable hierarchies) equations follow from the matrix model representation.

It has been realized recently that the c=1 conformal block of 4 point function in Liouville CFT is related to the Tau function of the Painlevé 6 integrable system. Here we propose a general construction: starting from a very general integrable system (a Hitchin system: the moduli space of flat G-connections over a Riemann surface, with G an arbitrary semi-simple Lie group), we define some « amplitudes », and we show that these amplitudes satisfy all the axioms of a CFT: they satisfy OPEs, Ward identities and crossing symmetry. The construction is very geometrical, by defining a notion of « quantum spectral curve » attached to a flat connection, defining homology and cohomology on it, and showing that amplitudes satisfy Seiberg-Witten like relations, and behave well under modular transformations.
So this link between CFTs and integrable systems unearths a new and beautiful quantum geometry.