My research interests include operator theory, Hilbert spaces, and non-commutative analysis. I also enjoy studying the connections between these fields and other branches of mathematics. My current project begins with the observation that an object from Hilbert space theory (the Szegő kernel) arises from computations in random matrix theory. With my PhD advisor, we have proven some generalizations which we expect will have interesting implications in random matrix theory. There is also further research to be done in understanding the connection between random matrix theory and Hilbert spaces.
Determinants of Random Unitary Pencils
(with M. Jury)
Journal of Functional Analysis 291 Issue 6 (2026) Paper no. 111555, 60 pages.