Research Statement

My broad area of research is in the interface of

Commutative Algebra, Algebraic K-theory, and Algebraic Geometry.

My specific interests are:

K-theory of monoid algebras and toric varieties/schemes and Projective Modules over commutative rings (vector bundles over affine schemes). Also, I am interested in homology stability of classical groups and its application to projective modules.

 I am interested in the problem of having rank one free summand (nowhere vanishing section) of projective modules

 (algebraic vector bundles) over singular affine algebras (affine schemes). Motivated by the works of  Asok-Fasel on this topic,

 I am also interested in A^1-homotopy theory,  Hermitian K-theory and its application to the (affine) algebraic geometry.

In my Ph.D. thesis, I have worked on projective modules over monoid algebras / affine toric varieties/schemes. More specifically, 

I study the problem of having rank one free summand (nowhere vanishing section) of projective modules (algebraic vector 

bundles) over monoid $R$-algebras (affine toric scheme over $\Spec(R)$) under some rank and dimension condition. 

These study naturally leads to the study of K-theory of toric varieties which is my current interest of research.

I have studied the Quillen K-theory over some affine singular toric schemes. I have also computed the Euler class group

(defined by S.M. Bhatwadekar and Raja Sridharan) of some commutative rings. To know more about my research work, 

please see the Publications .