About me and my research interest!

 Hi, I am Husney Parvez Sarwar. Welcome to my homepage!

I am an Assistant Professor  in the Department of Mathematics,
Indian Institute of Technology Kharagpur, India.

Research interest: My broad area of research is in the interface of algebraic K-theory, algebraic geometry and 
commutative algebra.  At present, I am interested in the K-theory of monoid algebras and toric varieties/schemes.
Motivated by the work of  Asok-Fasel, 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 (schemes).
Due to their work, I am also interested in A^1-homotopy theory,  Hermitian K-theory and it's applications to the
(affine) algebraic geometry.

In my 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|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
of some commutative rings. To know more about my research work, please see the research section.








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Husney Parvez Sarwar,
Dec 7, 2016, 6:24 AM
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