Ph.D. student, Mathematics
TIFR Centre for Applicable Mathematics, Bengaluru
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Teaching the Bolzano-Weierstrass theorem, SWIM 2025, Bengaluru.
I work on hyperbolic conservation laws, a species of nonlinear partial differential equations that generally take the form of a space-time divergence, i.e. $$\partial_t u + \nabla \cdot f(u) = 0.$$ I am fascinated by nonlinearity and its consequences for well-posedness, i.e. existence, uniqueness, and regularity of solutions. My present research focuses on the effects of spatial heterogeneity and non-local terms in hyperbolic conservation laws.
My core mathematical drive is developing sharp criteria for the behaviour of solutions to nonlinear PDEs. To this end, I enjoy monster-hunting: I love mapping the landscape of theories and techniques through various means, to demonstrate how the theory hinges on crucial assumptions. The absence of any totalising abstract framework encompassing all equations is the most delightfully frustrating aspect of nonlinear PDEs.
Please feel free to write to me, especially if you want to collaborate!
My advisor is Prof. Shyam Sundar Ghoshal.