My general area of research is "Theoretical and Computational Fluid Dynamics". Specifically my research work focuses on "Topological Fluid Dynamics."
Brief description of Topological Fluid Dynamics: Topological fluid dynamics is a young mathematical discipline that studies topological features of flows with complicated trajectories and their applications to fluid motions, and develops group-theoretic and geometric points of view on various problems of hydro-dynamical origin. It is situated at a crossroads of several disciplines, including Lie groups, knot theory, partial differential equations, stability theory, integrable systems, geometric inequalities, and symplectic geometry. One of the most intriguing observations of topological fluid dynamics is that one simple construction in Lie groups enables a unified approach to a great variety of different dynamical systems,from the simple (Euler) equation of a rotating top to the (also Euler) hydrodynamics equation, one of the most challenging equations of our time.
Currently, I am working in " Vortical Structures in 2D and 3D Separated Flows: A Topological Framework" under the supervision of Prof. Jiten Chandra Kalita.