I am a fourth-year PhD student in mathematics at IISER Thiruvananthapuram. My advisor is Md. Ramiz Reza (Aliah University, Kolkata), and my institutional advisor is Sheetal Dharmatti.
My research lies at the intersection of operator theory and complex function theory. I study Hilbert spaces of analytic functions, especially Dirichlet-type and de Branges–Rovnyak spaces, as well as weighted shifts on directed trees.
Papers
-
Wold-type decompositions for norm-increasing m-concave weighted shifts on directed trees
Preprint, 2026. arXiv
-
Higher order weighted Dirichlet type spaces with poly-superharmonic weights and Dirichlet type operators of finite order
With M. R. Reza. Preprint, 2025. arXiv
-
Toeplitz operators on the Dirichlet space and the Brown–Halmos operator identity
With M. R. Reza. Banach Journal of Mathematical Analysis, 2025. Article
Talks
-
Higher Order Weighted Dirichlet Spaces with Polysuperharmonic Weights and Dirichlet-Type Operators of Finite Order
Contributed talk, ACOTCA 2026.
University of Bologna, Italy.