Research

My broad research interests lie in algebra, specifically in the study of rings, and modules. Initially, I worked on finitely generated projective modules over commutative noetherian rings, specifically areas related to the Euler class of projective modules, which take values in the Euler class group.  Currently, I am working on other invariants such as Chow groups, Chow-Witt groups, Symplectic Witt groups and Grothendieck–Witt groups, and on their connections with Euler class groups, and broadly with projective modules. These groups arise naturally in algebraic K-theory. I am also enthusiastic about developing a geometric perspective for this field, utilizing the language of motivic homotopy theory.

• 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) 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. (published online) 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

• Splitting criteria for projective modules over polynomial algebras (with Mrinal Kanti Das) (in communication)

• Injective Stability for relative linear and symplectic $\mathrm{K_1}$-groups (with Kuntal Chakraborty) (in preparation)

• Chow-Witt groups and Euler class groups over certain smooth real algebraic varieties (with Jean Fasel) (in preparation)

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

• Projective modules and complete intersection ideals over affine algebras

• From Unimodular Rows to Zero Cycles over Real Varieties, Indian Institute of Technology Bombay (September 2025) 

• On unimodular rows over real varieties, Krea University (August 2025)

• Serre Dimension of a graded ring and a question of Lindel, Indian Institute of Technology Madras (March 2025)

• On conjectures of Eisenbud and Evans. Indian Statistical Institute, Kolkata (July 2024)

• Zero cycles and projective modules over singular real varieties. IINMM - 2024, Indian Institute of Science Education and Research Thiruvananthapuram (June 2024)

• On obstruction theory for splitting of projective modules. Indian Institute of Science Education and Research Bhopal (June 2024)

• Unimodular rows over positively graded rings. IINMM – 2023, National Institute of Science Education and Research Bhubaneswar (September - October 2023)

• Stability theorems for projective modules over positively graded domain. Indian Statistical Institute, Bangalore Centre (September 2023)

• Splitting criteria of projective modules on polynomial algebras over algebraically closed fields. CoCAAG 2023, Indian Institute of Technology Hyderabad (February 2023)

• On Murthy’s complete intersection conjecture. Indian Statistical Institute, Kolkata (July 2022)

• A monic inversion principle and splitting criteria of projective modules on polynomial extension over various base rings. Indian Statistical Institute, Kolkata (June 2022)

• Complete intersection ideals and orbit space of unimodular rows. Indian Statistical Institute, Kolkata (June 2021)

• Complete intersection ideals as sections of projective modules. Indian Statistical Institute, Kolkata (July 2019)

• Suslin's n-factorial theorem. Indian Statistical Institute, Kolkata (April 2018)

• Unimodular rows and a theorem of Seshadri. Indian Statistical Institute, Kolkata (April 2017)