Algebraic Geometry, Periods of motives
Reacting flows - modelling and simulations, reaction wave dynamics, chemical kinetics, model reduction, singular and regular perturbation theory
Number theory
Tilings, namely in the following issues: Flip spaces, Aperiodic tilings, Quasicrystals, Random tilings
Diophantine geometry, Drinfeld modules, abelian varieties
Strongly correlated systems. Ultracold atoms. Integrable models of Mathematical Physics.
Extreme statistics in Bose-Einstein condensates, dynamics of excitations following Quantum Quench, Kardar-Parisi-Zhang evolution of one-dimensional interacting bosons.
Max-plus algebra, tropical convexity, dynamic programming, discrete event dynamic systems, non-linear Perron-Frobenius theory
Representation Theory, Cluster Algebras, Number Theory
Mathematical logic, category theory, automated reasoning
Quantization, Quantum Groups and quantum algebras, Noncommutative Geometry, Integrable systems
Smooth and Hamiltonian dynamical systems, celestial mechanics, planar billiards, spectral rigidity
Spectral geometry, Extremal eigenvalue problems, Harmonic maps, Moduli spaces
Algebraic geometry, birational geometry, and existence of "good models".
PDE and dynamical systems
Complex systems, out of equilibrium physics and irregular geometries
Asymptotic problems on global fields, zeta-functions, error-correcting codes, sphere packings...
Higher dimensional class field theory and class field towers; Zeta functions; Explicit methods in arithmetic
Representation theory and its connections to Algebraic and Symplectic geometry and Combinatorics
Nonequilibrium Statistical Physics
Functionals of Brownian Motion
Statistical properties and their applications in physics and computer science.
Sorting and Search Algorithms in Computer Science
Understanding the asymptotic properties of random structures such as search trees in computer science using methods of statistical physics.
Extreme Value Statistics
The probability distribution of the maximum of a set of CORRELATED random variables with applications in Random Matrices, Fluctuating Interfaces, Longest Increasing Subsequence Problem and a class of Sequence Matching problems in biology.
Representation Theory of Lie groups
Algebraic methods in PDE, noncommutative determinants for semilinear systems, numerical methods for shallow water equations and Bénard-Marangoni instability
Statistiques intermédiaires et statistiques d'exclusion dans les systèmes d=1 et d=2. Effet Hall quantique entier et fractionnaire : transport et rôle du désordre. Systèmes désordonnes d=1 et d=2 : impuretés magnétiques
Quantum field theory and renormalization, in particular at the non perturbative level; Quantum gravity in particular discrete random tensor models and their relationship with Sachdev-Ye-Kitaev models; Non commutative field theory, random matrices
Statistical mechanics: extreme value statistics, non-equilibrium dynamics, first-passage problems and disordered systems.
Representation Theory, Combinatorics
Geometrical and topological combinatorics, graph colorings
Statistical Mechanics, Interacting particle systems and Gibbs measures
Mathematical physics, statistical mechanics
