Research

Research interests:  

My board area of research is in the confluence of Commutative Algebra and Algebraic K-theory.  More specifically, I focus on studying projective modules over commutative rings and monoid algebras. I am also interested in the theory of lower K-groups and the Euler class group, including their applications to projective modules. Recently, my research has focused on symplectic modules over the geometric subring of polynomial rings and monoid algebras.

 In my Ph.D. thesis, I have been investigating certain $\K$-theoretical properties of subrings of polynomial rings, such as $\K_{0}, \K_{1}, \K_{0}\Sp, \K_{1}\Sp$ stability. This includes examining how these tools can provide insights into the splitting, generation, and cancellation properties of projective and symplectic modules. 

Research Profiles:

Researchgate arXiv Google Scholar ORCiD 

Publications:

1. C. Bhaumik and H. P. Sarwar: Existence of unimodular element in a projective module over symbolic Rees algebras.  Proc. Math. Sci. 133, 47 (2023). https://doi.org/10.1007/s12044-023-00768-w 

2. S. Banerjee, C. Bhaumik and H. P. Sarwar: Efficient generation, unimodular element in a geometric subring of a polynomial ring, Journal of Algebra and its Applications.  25, no 09, 2650086 (2026). https://doi.org/10.1142/S0219498826500866 

3. C. Bhaumik, Md A. Raihan and H.P. Sarwar: Existence of unimodular elements and cancellation of projective modules over Rees-like algebras and its various extensions, To appear in International Journal of Algebra and Computation (IJAC). https://doi.org/10.1142/S0218196726500293 

Preprints:

4. C. Bhaumik, Manoj K. Keshari and H.P. Sarwar: Symplectic modules over geometric subrings and monoid algebras, Submitted.