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  • Spinorial representations of Lie Groups 
    JOSHI, ROHIT (Dept. of Mathematics, 2016-08)
    We solve the question: which finite-dimensional irreducible orthogonal representations of connected reductive complex Lie groups lift to the spin group? We have found a criterion in terms of the highest weight of the ...
  • Tightest Lower Bound for the Elliptic Curve Diffie-Hellman Problem and New Attacks on the Discrete Logarithm Problem 
    KUSHWAHA, PRABHAT (Dept. of Mathematics, 2017-02)
    The elliptic curve discrete logarithm problem(ECDLP) is one of the most widely used primitives in various public key cryptosystems. Hardness of ECDLP is an absolute security necessity, but not sufficient, for these ...
  • MOR cryptosystem with orthogonal groups 
    SHINDE, PRALHAD (Dept. of Mathematics, 2017-04)
  • Computations in Classical Groups 
    BHUNIA, SUSHIL (Dept. of Mathematics, 2017-04)
    In this thesis, we develop algorithms similar to the Gaussian elimination algorithm in symplectic and split orthogonal similitude groups. As an application to this algorithm, we compute the spinor norm for split ...
  • Fluctuations in the distribution of Hecke eigenvalues 
    PRABHU, NEHA (Dept. of Mathematics, 2017-04)
    A famous conjecture of Sato and Tate (now a celebrated theorem of Taylor et al) predicts that the normalised p-th Fourier coeffcients of a non-CM Hecke eigenform follow the Sato-Tate distribution as we vary the primes ...
  • Critical values of L-functions for GL3 × GL1 over a number field 
    SACHDEVA, GUNJA (Dept. of Mathematics, 2017-08)
    We prove an algebraicity result for all the critical values of L-functions for GL3 × GL1 over a totally real field, and a CM field separately. These L- functions are attached to a cohomological cuspidal automorphic ...
  • 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 ...
  • A study of Component-Wise Semi-Markov Process 
    YADAV, RAVISHANKAR KAPILDEV (2023-04)
    Component-wise semi-Markov processes (CSM) constitute a larger class of pure jump processes which includes semi-Markov, and Markov pure jump processes. This thesis examines semi-Markov as well as CSM processes with dependent ...

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