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  • Classical K-Theory: Completion of Unimodular Rows 
    MANDLIK, NISHAD (2015-05)
    In this thesis, we explore the problem of the completion of unimodular rows which has its historical importance in the solution of Serre's problem. We also study Classical Algebraic K-theory in the context of projective ...
  • Pricing in a semi-Markov modulated jump diffusion model 
    KRISHNA, AKASH (2015-05)
    In this thesis, we introduce a new market model for the stock price dynamics. It is a regime switching market where the parameters volatility and drift follows a semi-Markov process. In addition to that along with the ...
  • Statistical inference of semi-Markov process and application in Finance 
    NANDAN, SANKET (2015-05)
  • Function Field Sieve: Recent advances in the index-calculus attack on the discrete logarithm problem 
    K, HARIRAM (2015-05)
    In this paper we look into the discrete log problem over finite fields. The relative hardness of this problem defines the integrity of many cryptographic systems. Therefore the ease of solvalbility of this problem has been ...
  • Secret sharing schemes and application to e-voting 
    PREETI, P (2015-05)
    We present a way of sharing a secret S into n shares such that the collusion of any k shares results in the reconstruction of secret S and no k − 1 shares can do so. This way of sharing secret was first introduced by ...
  • Constructions of covering arrays 
    CHANDRASEKHARAN, RESHMA (2015-05)
    A covering array of size n, strength t, degree k and order g is a k n array on a set of g symbols with the property that in each t n subarray, every t 1 column appears at least once. Covering arrays have been studied for ...
  • Cohomology of GL(2) 
    P., SHIVA CHIDAMBARAM (2015-05)
    Let $F$ be a number field. Let $G=GL(2)$ over $F$. Let $\mathbb{A}$ and $\mathbb{A}_f$ denote the ring of adeles and finite adeles of $F$ respectively. Let $K_{\infty}$ denote the maximal compact subgroup of $G_{\infty}= ...
  • Inverse Galois Problem 
    SHUKLA, ABHISHEK (2016-04)
    In this thesis, motivated by the Inverse Galois Problem, we prove the occurence of Sn as Galois group over any global field. While Hilbert’s Irreducibility Theorem, the main ingredient of this proof, can be proved(for ...
  • Coleman map for the elliptic curve 
    KULKARNI, SAMEER (2016-05)
  • Asset Pricing in a Semi-Markov Modulated Market with Time-dependent Volatility 
    PATANKAR, TANMAY (2016-05)
    This project attempts to address the problem of asset pricing in a financial market, where the interest rates and volatilities exhibit regime switching. This is an extension of the Black-Scholes model. Studies of ...
  • A Study of Riemannian Geometry 
    SAFEER, K M (2016-05)
    In this reading project I studied some interesting results in Riemannian geometry. Starting from the definition of Riemannian metric, geodesics and curvature this thesis covers deep results such as Gauss-Bonnet theorem, ...
  • Topics in Algebraic Geometry 
    SAHANI, ABHINAV (2016-05)
    The key objective of this yearlong project was to learn serveral concepts in commuta- tive algebra and algebraic geometry. We started with learning concepts in commuta- tive algebra, which included primary decomposition, ...
  • Topics in Algebraic K-theory 
    K, ARUN KUMAR (2016-05)
    The objective of this thesis is to study the algebraic K-theory of exact categories. In algebraic K-theory we construct a sequence of groups, called K n , which are invari- ants of a given exact category. We look at two ...
  • Statistical Modeling of Extreme Events 
    PRASAD, BIRBAL (2016-05)
    Extreme value (EV) analysis involves the estimation of the probability of events that are unusually large or small. EV methods have a wide range of application from modeling extreme wave heights and water levels in hydrology, ...
  • Non-local equations: existence and multiplicity results 
    MUKHERJEE, DEBANGANA (Dept. of Mathematics, 2016-07)
    The main theme of my thesis is based on non-local type elliptic equations. In particular, existence of infinitely many nontrivial solutions for a class of equations driven by non-local integro-differential operator ...
  • 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 ...
  • Gap distribution among sequences arising in the theory of modular forms 
    PUJAHARI, SUDHIR (IISER PuneDept. of Mathematics, 2016-11)
    In the thesis, we have studied effective distribution of gaps between elements of one or more than one sequences. We also have studied a multiplicity one kind theorem for cusp forms.
  • On Cancellation Properties in Affine Geometry 
    MOHAMMAD, MUNAIF IQBAL AHMED (2016-12)
  • Covering Arrays and Generalizations 
    AKHTAR, YASMEEN (Dept. of Mathematics, 2016-12)
    Covering arrays have been successfully applied in the design of test suites for testing systems such as software, circuits, and networks, where failures can be caused by the interaction between their parameters. There has ...
  • Polynomial knots and their spaces 
    RAUNDAL, HITESH (Dept. of Mathematics, 2017-02)
    The main focus of this thesis is to study the topology of some spaces associated with polynomial knots and determining the least polynomial degree in which a given knot can be represented. A polynomial knot is an embedding ...

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