Ph.D.: Københavns Universitet (2023-)

MSc: Indian Insitute of Technology, Madras (2021-2023)

Master’s Thesis: “Spectrum of Laplacian on Hyperbolic Surfaces”

The main goal of my Master’s thesis was to obtain a complete understanding of the spectrum of the Laplacian on Hyperbolic Surfaces of infinite area. We began with the study of the upper-half plane, hyperbolic surfaces, hyperbolic ends, and decompositions of the spectrum. Later we defined the Laplacian on an arbitrary manifold and discussed one of the important theorems: “The Laplacian on a complete Riemannian manifold is essentially self-adjoint”. Finally, we described the spectrum for the Upper half plane and the characterizations of the essential and the discrete spectrum on Hyperbolic Surfaces.