Mathematics
My research is broadly situated in the pure and applied analysis of partial differential equations (PDEs) and in the area of control and dynamical systems, with a particular focus on stabilization, well-posedness, and applications.
- Stabilization of Linear and Nonlinear PDEs: Studying the stabilization of abstract PDEs, feedback stabilization, and the preservation of exponential stability under perturbations, with applications to singular and degenerate parabolic PDEs, interacting elastic systems of plates and membranes governed by coupled PDEs, and other related systems, etc.
- Well-posedness of PDEs: Existence, uniqueness, and regularity of solutions to linear and nonlinear PDEs, such as the generalised Burgers–Huxley equation, the generalised Korteweg–de Vries–Burgers–Huxley equation, the damped viscous Burgers equation, Maxwell’s equation systems, etc.
- Numerics of PDEs: Numerical schemes for controlled and uncontrolled PDEs, focusing on how discretization interacts with stability and control properties. This includes investigating the effectiveness of spectral methods compared to other approaches.
Beyond Mathematics
My independent research interests include, but not limited to:
- Indian Philosophy: Classical Indian philosophical traditions, with focus on comparative analysis, polemics, epistemology, metaphysical frameworks, and ethics.
- Consciousness Studies: The intersection of philosophy, theoretical neuroscience, and neurophenomenology.
- Philosophy and Artificial Intelligence: Investigating the conceptual foundations linking philosophy and AI, including questions of intelligence, autonomy, and the possibility of artificial consciousness.
- Bioinformatics: Mathematical modeling, computational analysis, and inference from biological data.