Faculty Research Interests
The research interests of the faculty at the School of Mathematics, IISER-TVM span a wide range of areas. These include linear algebra, positive operator theory, partial differential equations, stochastic processes, numerical functional analysis, financial mathematics, control theory, differential games, combinatorial number theory and Ramsey theory.
Dr. Sachindranath Jayaraman’s research interests are in linear algebra, particularly in the theory of generalized inverses of linear operators (both in finite and in infinite dimensional spaces). More specifically, he is interested in the interplay between the nonnegativity of various generalized inverses and the geometry of the underlying cones.
Dr. Utpal Manna works in nonlinear partial differential equations arising mostly from fluid dynamics (e.g. Navier Stokes equations, vorticity equations, shell model of turbulence, magneto-hydrodynamic systems etc.) driven by a Wiener process or other Levy processes. He studies existence, uniqueness, regularity, large deviation and control of these fluid models using tools from stochastic analysis, harmonic analysis, nonlinear functional analysis and PDE theory.
Dr. M.P. Rajan’s research focuses on numerical solution of inverse and ill-posed problems. The idea is to get stable approximate solutions for problems that are ill-posed in nature. He also works on a certain class of parameter identification problems in nonlinear PDEs. Dr. Rajan is also interested in financial engineering and mathematical finance, multidisciplinary research areas that focus on developing financial models that integrate financial theory, methods of engineering, tools of mathematics and the practice of programming.
Dr. Dharmatti Sheetal’s research interest is in partial differential equations. She works mainly on control theory and game theory problems arising through ordinary and partial differential equations. The solution to such problems are determined by using viscosity solution theory, a notion of weak solution of PDEs. Dr. Sheetal also works on control of Navier Stokes equations and various problems related to it. Recently she has initiated work on image processing using PDE techniques.
Dr. Sujith Vijay’s area of research is Ramsey theory, a branch of combinatorics where the goal is to determine the least size of a host structure H with the property that any partition of H yields a regular substructure of specified size. When H is a finite initial segment of positive integers, and the substructures are arithmetic progressions of a given length, the sequence of minimal host structure sizes are called Van der Waerden numbers. Dr. Vijay’s recent work uses probabilistic techniques to obtain bounds on the analogue of Van der Waerden numbers for generalisations of arithmetic progressions and for random partitions.