Currently, I am interested in working on some parts of the classification program of distinguishing smooth, orientable, closed and simply-connected (SOCSC) 4-manifolds upto diffeomorphism. Some part of my research also explores (co)homological and homotopical aspects of certain non-associative algebraic invariants appearing in high-dimensional knot theory.
Additionally, I am quite interested in learning about other related topics, especially homotopy theory, characteristic classes, the Yang-Baxter equation, and the fascinating interplay of these with my current work.
Publications:
(with Deepanshi Saraf and Mahender Singh) Generalized (co)homology of symmetric quandles over homogeneous Beck modules.
Journal: Journal of Pure and Applied Algebra Volume 229, Issue 6, June 2025, 107956.
(with Deepanshi Saraf and Mahender Singh) Automorphisms, cohomology and extensions of symmetric quandles.
Journal: Homology Homotopy Appl. (2025), to appear.
(with Deepanshi Saraf and Mahender Singh) Generalized Legendrian racks of Legendrian links.
Journal: Journal of Topology and Analysis (2025), to appear.
Preprints:
(with Deepanshi Saraf and Mahender Singh) Beck modules over generalised Legendrian racks, submitted.
In Preparation:
(with Pragya Belwal and Mahender Singh) On the Homology of Set-Theoretic Solutions of the Yang-Baxter Equation.