Research Interests
The research carried out by our group is often inspired by questions of the following type:
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How can heuristics from theoretical physics be leveraged to help reveal new connections between seemingly disparate areas of mathematics?
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What mathematical structures are needed to describe Nature at the smallest scales?
Research interest focuses on two topics, namely Geometry and Mathematical physics. In geometry, questions about minimal surfaces (in R^3 for e.g. idealized soap films) and maximal surfaces (in Lorentz-Minkowski 3-space, say) are studied. In mathematical physics, interests include various notions of quantization, particularly geometric quantization, and its application to the study of moduli-spaces of solutions of equations arising from physics, as well as certain integrable systems.
Pranav's work explores mathematical structures underlying quantum field theory and string theory using the language of higher category theory and derived geometry.
Research interests include areas of theoretical physics such as general relativity, classical mechanics of constrained systems, classical and quantum optics, statistical mechanics of soft matter and quantum Information. The unifying theme being differential geometry and topology in physics.
Research interests include Lie groups and Arithmetic groups.