I obtained by doctorate from Louisiana State University, in 2022, under the supervision of Gestur Olafsson. After that, I completed a 3-year postdoc at Clemson University, with Mishko Mitkovski. Starting from August, 2025, I am a visiting assistant teaching professor in the Department of Mathematics at the College of William & Mary.
My current research focuses on understanding Toeplitz operators using quantum harmonic analysis (QHA).
Other than math, I like to spend time in nature. Occasionally, I paint. I am very slowly learning to play the bass.
Contact me at: vdewage@wm.edu
My research: My current research uses quantum harmonic analysis (QHA) to answer questions in operator theory. In some of my joint works, we discuss the Laplacian, heat equation, and the heat semigroup for operators, and their applications to Toeplitz operators. We have also extended QHA techniques to the noncommutative setting of the Bergman spaces, over the unit ball and more generally over bounded symmetric domains, and then use the tools we formulate to clarify existing theorems on Toeplitz operators while also obtaining new ones.
Publications
V. Dewage, R. Fulsche and G. Olafsson, The function-operator convolution algebra over the Bergman space of the ball and its Gelfand theory (Submitted) arXiv link
V. Dewage, Toeplitz algebra of bounded symmetric domains: A quantum harmonic analysis approach via localization. J Funct. Anal. (2026) arXiv link
V. Dewage and M. Mitkovski, On the density of Toeplitz operators in the Toeplitz algebra over the Bergman space of the unit ball. (2025) arXiv link
V. Dewage and M. Mitkovski, A quantum harmonic analysis approach to the Berger-Coburn theorem. N.Y.J. Math, 31:887–901, (2025) arXiv link
M. Dawson, V. Dewage, M. Mitkovski and G. Olafsson, Quantum Harmonic Analysis on the Unweighted Bergman Space of the Unit Ball. Integr. Equ. Oper. Theory 97 (23) (2025) arXiv link
V. Dewage and M. Mitkovski, The Laplacian of an operator and the radial Toeplitz algebra. J. Math. Anal. Appl. 547 (1), paper no. 129245 (2025) arXiv link
V. Dewage and M. Mitkovski, Density of Toeplitz operators in rotation-invariant Toeplitz algebras. J. Fourier Anal. Appl., 31 (57), (2025). arXiv link
V. Dewage and G. Olafsson, Toeplitz operators on the Fock space with quasi-radial symbols. Complex Anal. Oper. Theory 16 (4), Paper no. 61, 32 pp. (2022) arXiv link
Quantum Harmonic Analysis (QHA): In QHA, introduced by Werner in 1984, we adopt notions from classical harmonic analysis, such as convolutions and Fourier transforms, for operators via representation theory. This perspective makes the way for a more elegant and intuitive approach to managing certain classes of operators, such as Toeplitz operators, pseudo-differential operators, and localization operators, providing an effective set of tools at the intersection of time-frequency analysis, mathematical physics, and operator theory.
At College of William & Mary
Fall 2025 - Math 302 - Differential equations (2 sections)
Fall 2025- Math 108 - Business Calculus
At Clemson University
Fall 2024 - Math 1010 - Essential Mathematics for the Informed Society (2 sections)
Spring 2024 - Math 4540 - Advanced Calculus II
Fall 2023 - Math 4350 - Complex Analysis
Fall 2023 - Math 4630 - Real Analysis
2022-2024 - Math 3110 - Linear Algebra (6 sections)
At Louisiana State University
Spring 2022 - Math 1021 - College Algebra
Fall 2021 - Math 1550 - Analytic Geometry & Calculus - I
Summer 2021 - Math 1552 - Analytic Geometry & Calculus - II (75-99% Web based)
Spring 2021 Math 1550 - Analytic Geometry & Calculus - I (100% Web based)
Fall 2020 - Math 1021 - College Algebra (100% Web based)
Summer 2019 - Math 2057 - Multidimensional Calculus
Summer 2018 - Math 1552 - Analytic Geometry & Calculus - II
Fall 2017 - Math 1021 - College Algebra