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  • Martingale Optimal Transport and Portfolio Theory 
    KUMBHAR, VRUSHALI (2019-04)
    This project involved the study of Monge-Kantorovich problem of optimally transporting one distribution of mass to another. A cost is incurred while doing the transportation and the optimality is measured against this cost ...
  • Lipschitz Extension Problem 
    GHUMMAN, MANRAJ (2021-06)
    This project is mainly concerned with the understanding of the problem of extending Lipschitz functions from the boundary of some set to inside it in some special way. This extension is minimal/least fluctuating in some ...
  • Stochastic Partial Differential Equations 
    SURENDRANATH, SUDHEESH (2021-06)
    In this thesis, we study the random-field approach for solving a class of parabolic stochastic partial differential equations and study some properties exhibited by their solutions, some of which include intermittency, ...
  • Study of Poincaré-Hardy type inequalities and eigenvalue problems for second-order elliptic PDEs 
    ROYCHOWDHURY, PRASUN (Dept. of Mathematics, 2022-03)
    The major text of this thesis is studying Poincaré-Hardy and Hardy-Rellich type inequalities on one of the most discussed Cartan-Hadamard manifold namely hyperbolic space and studying eigenvalue problems for second-order ...
  • Regularity theory of integro-differential operators and its application 
    MODASIYA, MITESH (2024-01)
    Integro-differential operators arise naturally in biological modeling and mathematical finance. We aim to conduct an in-depth study of integro-differential operators and their regularity properties in this thesis. We start ...
  • Nonlocal Ergodic Control Problem with Near-monotone Cost 
    MUSUNURI, BHAVANA (2024-05)
    This thesis aims to provide an overview of the Integro-differential equations of fractional type and the associated regularity results for the viscosity solution. In the second part of the thesis, we consider a nonlocal ...

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