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.
Bethe ansatz / Yang-Baxter equation
ideas applied to exactly solvable lattice models
(six vertex and other square ice type models)
and quantum integrable stochastic systems.
In Spring 2016 (January 20 — May 3), my
office hours are
- Monday, 3:30pm—4:30pm
- Wednesday, 11:00am—12:00pm
Office: 209 Kerchof Hall
no. 22 at the Campus Map
MATH 8380: Random Matrices
which meets on Mondays and Wednesdays, 2:00-3:15PM, in Kerchof 317.
Course webpage on GitHub