PERSONAL SITE

I am currently an Assistant Professor Grade-I in the Department of Mathematics at Indian Institute of Technology (IIT) Indore (since 15th March 2023 onwards).

 My areas of research lie in the following:

​

• Probability Theory and Stochastic Processes

• Stochastic Analysis: Invariant measures, Ergodicity, etc;

• Stochastic (Partial) Differential Equations: Local and global solvability, Support theorems, etc;

• Partial Differential Equations: Solvability, stability, and asymptotic behaviour of elliptic, parabolic, and hyperbolic systems;

• Control Theory: Deterministic and stochastic control theory in finite and infinite dimensions, Optimal control theory, etc;

• Mathematical Fluid Dynamics: Solvability of compressible and incompressible fluid flow equations, asymptotic analysis, stochastic analysis, controllability of fluid flows, etc (e.g. viscoelastic fluid ow equations, solid-fluid interaction problem).

•  Mathematical Aspects of Pattern Formation in Biological Systems: Local and global solvability of stochastic cross-diffusion system and chemotaxis Keller-Segel system;

• Study of Ferro-magnetism: Local and global solvability of Landau-Lifshitz-Gilbert-Equations; Controllability of LLGE etc;

• Shape calculus approach for solving exterior boundary value problems.