Research

"It doesn't matter how long it takes, if the end result is a good theorem."

-John Tate

Current Work (PhD)

I am mainly interested in the area of Homological Algebra, Algebraic geometry, Mackey functors, Finite group Representations, Galois Cohomology, K-theory, and skew field theory. I am currently working on two different research problems:

On the converse of Donkin's Conjecture
Classification of higher dimensional tori and toric varieties over an arbitrary field.

Publications/Preprints

On the weak Lefschetz property for ideals generated by powers of general linear forms (with Matthew Booth and Adela Vraciu)(Submitted) (arxiv link)
Classification of higher dimensional tori (in preparation)

Masters' Thesis

Aug 2019 - June 2020: Connectivity of the tropical double ramification cycle, Supervision of Dr. Dmitry Zakharov, CMU, Department of Mathematics, Michigan, United States.

(In this master’s thesis, we studied the connectivity properties of a polyhedral object known as the tropical double ramification DR cycle. We proved that the tropical DR cycle has the same connectedness property for a particular choice of parameters. )

Expository Articles On Mackey Functors (It may contain some error: Please let me know if you see any)

These are the notes I made to understand the materials at the start of my project:

Theory_Of_Cohomological_Mackey_Functors.pdf