Ktheories are very important invariant associated to the algebras, varieties, schemes and spaces.
I work on Ktheory of monoid algebras and toric varieties.
My another area of research is projective module over affine algebras, i.e.,
vector bundles over affine schemes. This is "essentially" a study of lineal algebra
over commutative rings with 1. Projective modules are "locally" free module.
Free modules over commutative rings are those modules which have a basis.
Then one would like to investigate 'how far" a projective module from being
a free module. Starting point of all these is a famous conjecture of J.P. Serre.
The statement is "every projective modules over polynomial rings are free".
This is now a theorem due to Quillen and Suslin. The "equivalent" question in
linear algebra is: given a vector (a_1,...a_n) in R^n (here R is a commutative
ring with 1) such that a_1b_1+...+a_nb_n=1, then can we write down (or find
in an existential way) nxn invertible matrix such that first row is (a_1,...,a_n)?
Here is the link for JRF recruitment: http://www.iitkgp.ac.in/temporaryjobs (2nd adv. from the last)

Ktheory of monoid algebras and a question of Gubeladze Sarwar H. P., Krishna A. By Journal of the Institute of Mathematics Jussieu 18 10511085 (2019)

Ktheory of monoid algebras and a question of Gubeladze Sarwar H. P., Krishna A. By Journal of the Institute of Mathematics Jussieu 18 10511085 (2019)

Negative Ktheory and Chow group of monoid algebras Sarwar H. P., Krishna A. By KTheory Conference (AMS, Contemporary Mathematics) 195224 (2020)

Negative Ktheory and Chow group of monoid algebras Sarwar H. P., Krishna A. By KTheory Conference (AMS, Contemporary Mathematics) 195224 (2020)

Stability results for projective modules over Rees algebras Sarwar H. P., Rao R. A. By Journal of Pure and Applied Algebra 223 19 (2018)

Stability results for projective modules over Rees algebras Sarwar H. P., Rao R. A. By Journal of Pure and Applied Algebra 223 19 (2018)

Some results about projective modules over monoid algebras Sarwar H. P. By Communications in Algebra 44 22562263 (2016)

Some results about projective modules over monoid algebras Sarwar H. P. By Communications in Algebra 44 22562263 (2016)

Serre dimension of monoid algebras Sarwar H. P., Keshari M. K. By Proc. of Mathematical Sciences (Indian acad Sci.) 127 269280 (2017)

Serre dimension of monoid algebras Sarwar H. P., Keshari M. K. By Proc. of Mathematical Sciences (Indian acad Sci.) 127 269280 (2017)
Principal Investigator
 Homology stability of classical groups and its application to projective module and Ktheory
Ph. D. Students
Chandan Bhaumik
Area of Research: Algebraic Ktheory
Md Abu Raihan
Area of Research: Algebraic Ktheory
Sudip Manna
Area of Research: Algebraic Geometry