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  • Harmonic analysis on locally symmetric spaces associated to cocompact discrete subgroups of SL2(R) 
    NAIR, AJITH (2017-04)
    In his 1956 paper, Selberg proved the famous Trace Formula for a semisimple Lie group G and its discrete subgroup 􀀀. The case when G = SL2(R) is quite well-known. In this thesis, we look at the decomposition of L2(􀀀nG) ...
  • Class Field Theory 
    SINGH, SHASHANK (2018-05)
    In this thesis, we state and sketch the proofs of main theorems of class field theory. There are many approaches to studying class field theory. We take the cohomological approach to prove the main results for the local ...
  • On Spectra of Graphs and Manifolds 
    FATIMA, AYESHA (Dept. of Mathematics, 2019-01)
    One can define the notion of primitive length spectrum for a simple regular periodic graph via counting the orbits of closed reduced primitive cycles under an action of a discrete group of automorphisms. We prove that this ...
  • Spectral Graph Theory 
    HINGE, AMOL SAHEBRAO (2019-04)
  • From Tate’s Thesis to Automorphic ForMS and Representations on GL(2) 
    MISTRY, RAHUL (2019-05)
    In this thesis we look at the celebrated Riemann-Zeta function and its generalizations and Tate’s famous thesis which gave a way to arrive at the functional equations and meromorphic continuouations of such functions. ...
  • Representation theory of p-adic groups and the local Langlands correspondence for GL(2) 
    V., NAZIA (2020-04)
    We discuss the representation theory of GL(2, F), where F is a non-archimedean local field following 'The Local Langlands Conjecture for GL(2)' by Bushnell and Henniart. Then we look at the decomposition of L^2(H\PGL(2, ...
  • On the cuspidal cohomology of ${\rm GL}_4$ 
    MONDAL, SUDIPA (Dept. of Mathematics, 2022-04)
    In this thesis, we estimate the contribution of symmetric cube transfer and tensor product transfer to the cuspidal cohomology of ${\rm{GL}_4}$. Let $\mathbb{E}=\mathbb{Q}(\sqrt{-d})$ be an imaginary quadratic extension ...
  • Analysis and Arithmetic of p-adic Numbers 
    DEY, PRIYANKA (2024-05)
    p-adic numbers play an important role in modern number theory. They encode important information about congruences between integers. From rational number, one construct the smallest complete field that contains rational ...

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