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. I am 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. Notably, the C*-algebra machinery that proved effective in the Drury-Arveson setting fails to extend to the Fock space. This limitation has motivated me to explore alternative methods, potentially involving free probability techniques and other non-commutative analytical tools, to achieve meaningful results in this challenging environment.