Most of my research revolves around probabilistic models which are "integrable" (or "exactly solvable"), in the sense that they possess an underlying algebraic structure.
The latter provides powerful tools for analysis of such models, and allows to investigate their deep properties which are inaccessible by purely probabilistic methods.
In problems I am interested in,
integrability mainly comes from the following diverse sources:
Representation theory of "big" groups, such as the infinite symmetric group, or the infinite-dimensional unitary group. This subject is also naturally related to branching graphs, such as the Young graph, i.e., the lattice of all Young diagrams ordered by inclusion.
Formalism of determinantal/Pfaffian point processes.
Deep properties of symmetric polynomials, most notably, the Macdonald polynomials with parameters (q, t) and their various degenerations, including the classical Schur polynomials arising for q = t.