Spectral theory of quasiperiodic and ergodic Schrödinger operators
Inverse spectral theory of differential operators
Spectral theory of quantum graphs
Potential theory, Chebyshev polynomials, orthogonal polynomials
Complex function theory
Spectral bounds for ergodic Jacobi operators; preprint (2024) [arXiv]
On the spectra of periodic elastic beam lattices: single-layer graph; with M. Ettehad, Journal of Spectral Theory (accepted for publication) (2025) [arXiv]
Uniqueness theorems for meromorphic inner functions and canonical systems; Canadian Mathematical Bulletin, 68 (1) , 124 - 140 (2025) [Journal] [arXiv]
(Sub)critical operators and spectral capacities of rational frequency approximants; with S. Jitomirskaya, Journal of Mathematical Physics, Analysis, Geometry 20, 498-514 (2024) [Journal]
Spectral bounds for periodic Jacobi matrices; Proceedings of the American Mathematical Society 152 (9), 3915-3922 (2024) [Journal] [arXiv]
On meromorphic inner functions in the upper half-plane; in Function Spaces, Theory and Applications, Fields Institute Communications 87, 229-243 (2023) [Proceeding]
Ambarzumian-type problems for discrete Schrödinger operators; with J. Eakins, W. Frendreiss, L. Lamb, S. Manage, A. Puente. Complex Analysis and Operator Theory 15, 118 (2021), part of the collection Spectral Theory and Operators in Mathematical Physics [Journal] [arXiv]
Mixed data in inverse spectral problems for the Schrödinger operators; Journal of Spectral Theory 11 (1), 281-322 (2021) [Journal] [arXiv]
Inverse problems for Jacobi operators with mixed spectral data; Journal of Difference Equations and Applications 27 (1), 81-101 (2021) [Journal] [arXiv]
Some asymptotics for extremal polynomials; with G. Alpan, A. Goncharov, in Computational Analysis: Contributions from AMAT, Springer Proceedings in Mathematics & Statistics 155, 87-101 (2016) [Proceeding]
Widom factors; with A. Goncharov, Potential Analysis 42, 671-680 (2015) [Journal]
Colloquium, University of Michigan-Dearborn, February 2025
Analysis seminar, Vanderbilt University, November 2024
Analysis seminar, University of Wisconsin-Madison, October 2024
Spectral theory and applications conference, Texas A&M University, October 2023
Ergodic operators and quantum graphs workshop, Simons Center for Geometry and Physics, June 2022
Almost-periodic spectral problems workshop, Banff International Research Station, April 2022
Analytic function spaces and their applications focus program, The Fields Institute for Research in Mathematical Sciences, December 2021