My primary research interests lie in Functional Analysis, Operator Theory, Non-commutative Function Theory, and related areas. Currently, I am investigating Szegő-type limit theorems in multivariable complex vector spaces using operator-theoretic techniques. This work explores the interplay between functional analysis and multivariable operator theory, with potential applications to various mathematical and physical systems.

The classical Szegő theorem analyzes the eigenvalue distribution of Toeplitz matrices. I extended these ideas to the Drury-Arveson space, exploring new versions and generalizations of this result. As a corollary, we obtain similar results for regular unitarily invariant spaces.

I am currently investigating a similar problem in the Fock space, which represents a non-commutative counterpart to the Drury-Arveson space. The Fock space, widely studied in free probability and quantum mechanics, presents unique challenges due to its inherently different structure. However, I have found connections of the Szego Limits of multi-Toeplitz operators to the limiting distribution of random graphs, which is what my current research focuses on.