I am interested in new paradigms explaining old and new results in Random Matrix Theory (convergence towards the Tracy-Widom distribution via new hidden structures and analysis of functionals of the characteristic polynomial of a random Haar-distributed matrix), random partition theory (the same but with the Schur measure) and statistical mechanics of phase transitions (Curie-Weiss and one-dimensional Ising model studied with surrogates or new integrable structures). I am also interested in Symmetric Functions theory and in particular their probabilistic representations.

Algebras with polynomial identities, Integrable equations

Complex Geometry and Analysis, Hodge Theory, Non-commutative Geometry, Homological Mirror Symmetry

Modal logic, Boolean function complexity.

Endomorphism semirings, Matrix semirings, Derivations in semirings, Combinatorics, Stochastic processes.

Group algebras and Abel groups, modules and associative rings, algebraic theory of matrices.

Algebra: Theory of Associative Rings: fields; field extensions; Galois theory - maximal p-extensions, absolute Galois groups; central simple algebras; Brauer groups of fields - structure and invariants; valuation theory. Number Theory - local class field theory.

Representation theory of Lie algebras and Lie groups, applications to Invariant theory, infinite-dimensional Lie algebras, momentum maps, geometric quantization and applications to physics.

String theory, AdS/CFT correspondence, lattice gauge theories, Monte Carlo simulations, financial mathematics.