The subject of my research is theoretical physics/applied mathematics and I like to interpret is as broadly as possible. A very brief introduction to my research is below.
Natural systems are nonlinear, out of equilibrium, and span multiple spatial and temporal scales. Such complex systems arise in diverse contexts -- from biophysics and neuroscience to turbulence and multiphase flows. Frequently the governing equations at small scales are known (e.g., Navier-Stokes, Hodgkin-Huxley), The challenge lies in deducing the emergent behavior at large scales. This difficulty stems from three sources. First, the underlying equations are nonlinear and rarely solvable analytically. Second, collective behavior often yields emergent phenomena not evident at smaller scales (e.g., consciousness from neural interactions). Third, these systems typically operate far from equilibrium, exhibiting large, non-Gaussian fluctuations. My research spans analytical methods (asymptotics, stochastic calculus, multifractals) and numerical techniques (spectral, finite difference, Monte Carlo, machine learning) for such nonlinear multiscale problems. I am also a core developer of the Pencil Code, widely used in astrophysics.
I move into new areas of applications every seven-eight years. Over the last five years, I have worked on problems in astrophysics, geophysics, fluid/solid mechanics, active matter, and biophysics. Examples have appeared in Astrophysical Journal, Physical Review Letters, Physical Review E, Physical Review Research, Nature Communications, Science Advances, and Proceedings of National Academy of Sciences. My ongoing and future research involves development of numerical tools and analytical techniques for four interconnected applications: Nanoscale Biology, Neuroscience, Turbulence and Geophysical and Astrophysical Fluid Dynamics (GAFD).
A short description of my PhD thesis is here.