2- I Inégalités faibles de Morse
A brief review of supersymmetric non-linear sigma models and generalized complex geometry
This is a review of the relation between supersymmetric non-linear sigma models and target space geometry. In particular, we report on the derivation of generalized Kähler geometry from sigma models with additional spinorial superfields. Some of the results reviewed are: Generalized complex geometry from sigma models in the Lagrangian formulation; Coordinatization of generalized Kähler geometry in terms of chiral, twisted chiral and semi-chiral superfields; Generalized Kähler geometry from sigma...
A partial solution for Feynman's problem – a new derivation of the Weyl equation.
Affine Poisson groups and WZW model.
Définition de l'intégrale de Feynman et processus à sauts
Deformations of (bi)tensor categories
Dualités de champs et de cordes
Dynamical symmetries in supersymmetric matrix models.
Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model
Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986 [8], is a random process which takes values in the vertex set of a graph and is more likely to cross edges it has visited before. We show that it can be represented in terms of a vertex-reinforced jump process (VRJP) with independent gamma conductances; the VRJP was conceived by Werner and first studied by Davis and Volkov [10, 11], and is a continuous-time process favouring sites with more local time. We calculate,...
Extension of the Poincaré symmetry and its field theoretical implementation.
Finite unification: theory and predictions.
Free field construction of D-branes in rational models of CFT and Gepner models.
Generalized Heisenberg algebras, SUSYQM and degeneracies: infinite well and Morse potential.
Ground states of supersymmetric matrix models
We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in . Moreover, it would be unique. Other values of , where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation. This seminar...
Harmonic superfields in supersymmetric quantum mechanics.
Hopf maps, lowest Landau level, and fuzzy spheres.
Infinite-dimensional Lie groups and algebras in mathematical physics.
Mathematical structures behind supersymmetric dualities
The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.
Mirror symmetry and toric geometry.
Modular symmetry and fractional charges in supersymmetric Yang-Mills and the quantum Hall effect.