Research

My broad research interests lie in algebra, specifically in the study of rings, and modules. I am particularly interested in problems related to finitely generated projective modules over commutative noetherian rings. This can be reinterpreted geometrically as algebraic vector bundles over affine algebraic varieties. Initially, during my PhD and early postdoctoral years, I worked on areas related to the Euler class of projective modules, which takes values in the Euler class group. Currently, I am trying to understand other (invariant?) groups such as Chow groups, Chow-Witt groups, Symplectic Witt groups (or more generally Grothendieck–Witt groups), and on their connections with Euler class groups, and broadly with projective modules. These groups arise naturally in Algebraic & Hermitian K-theory. 

• Splitting criteria for projective modules over polynomial algebras (with Mrinal Kanti Das) J. Lond. Math. Soc., vol. 112, Issue 6, December 2025, e70369. DOI: 10.1112/jlms.70369

• Zero cycles, Mennicke symbols and $\mathrm{K}_1$-stability of certain real affine algebras Int. Math. Res. Not. IMRN, vol. 2025, Issue 15, August 2025, rnaf211. DOI: 10.1093/imrn/rnaf211

• Stability theorems for positively graded domains and a question of Lindel Kyoto J. Math., (accepted in 2025) DOI: 10.1215/21562261-2025-0008 (see this for the latest update)

• Analogies of monic inversion principles in Laurent polynomial rings (with Mrinal Kanti Das) J. Algebra, vol. 669 (2025), 220-242. DOI: 10.1016/j.jalgebra.2025.02.004

• Efficient generation, unimodular element in a geometric subring of a polynomial ring (with Chandan Bhaumik and Husney Parvez Sarwar) J. Algebra Appl., vol. 25, no. 9 (2026) 2650086 DOI: 10.1142/S0219498826500866

• Subrings of polynomial rings and the conjectures of Eisenbud and Evans J. Algebra, vol. 641 (2024), 85-104. DOI: 10.1016/j.jalgebra.2023.10.039

• On a question of Nori: Obstructions, improvements, and applications (with Mrinal Kanti Das) J. Algebra, vol. 635 (2023), 271-299.  DOI: 10.1016/j.jalgebra.2023.08.003

• Improved injective stability for relative $\mathrm{K_1Sp}$-groups (with Kuntal Chakraborty) arXiv: 2604.09476

• Suslin's cancellation conjecture on smooth real affine varieties with few real points (with Jean Fasel and Samuel Lerbet) arXiv: 2608.17890

• Projective generation of curves (IV) (with Soumi Tikader) (in preparation)

• Chandan Bhaumik

• Kuntal Chakraborty

• Mrinal Kanti Das

• Jean Fasel

• Samuel Lerbet

• Husney Parvez Sarwar

• Soumi Tikader