Research
A running account of what I'm working on and what I'm reading toward. Write to me if any of it overlaps with your own work — I'd rather talk than publish quietly.
Supervised by Prof. Swarnendu Sil. The work sits where geometric analysis meets gauge theory: how the Yang–Mills functional behaves on four-dimensional manifolds, and what that behaviour says about the underlying topology.
Alongside the thesis I'm studying topological K-theory under Prof. Mihir Sheth.
Spectra and the Adams spectral sequence, worked through with an eye on physics: which invariants are stable, and which of them a physical theory can actually see.
Topological quantum field theories, Costello's effective field theory and generalized cohomology in the Stolz–Teichner paradigm — and how diffeomorphism and conformal invariance might be understood through one cohesive topological lens.
Projects
Exploring the topological properties of the map φ′ : M → ΣA, using suspensions and adjunctions to move the system into the loop space of the spacetime manifold M. The work treats the underlying structure as a loop-space fibration of M and asks what the James construction J(M) implies for fundamental quantum gravity frameworks.
Advisor: Dr. B. S. Ramachandra.
Investigating structural relations between distinct fibrations that share a common base space, using Serre spectral sequences alongside the EHP sequence.
Advisor: Dr. B. S. Ramachandra.
Constructing a rigorous path mapping the Čech cohomology of positive solutions of the zero rest mass equations to singular homology representations, and using Serre spectral sequences to derive structural insight into the path-connectedness of the loop space within the solution space.
January 2026 – present
Developing a mathematical framework that expresses spin networks explicitly using twistors assigned to the network edges.
With Rahul K. Balaji, Meenakshi Venkatadri, Charu Gupta.
Explored methods for parameterizing the n-Yoneda lemma by way of the classical Yoneda lemma, and evaluated its deeper connections to Isbell duality.
With Rahul K. Balaji. August 2025 – November 2025
How does n-Yoneda behave? (PDF, 8 pages)Derived the geometric and physical conditions under which (3+1) gravity can be modelled as the boundary theory of a five-dimensional manifold.
With Rahul K. Balaji. June 2024
Technical projects
Built and optimised decision trees, random forests, gradient-boosted trees (XGBoost) and FastBDT to classify five particle event types from simulated Belle II detector data.
Course project, IISER Mohali. August 2025