My research interests broadly lie in category theory and generalized algebraic geometry. My works develop categorical approach to classical algebra and geometry, by bringing several aspects of enriched category theory and coalgebra theory together. I have developed interests in DG-categories and tensor triangular geometry since last couple of years. In a recent work, I have developed a general noncommutative version of Balmer’s tensor triangular spectra and support using coherent frames and locales. Presently, I am exploring connections between DG-categories and relative Hopf algebras. I am also actively working in the field of Absolute Algebraic Geometry or F1- geometry, which is algebraic geometry over more general algebraic structures than commutative rings, like for example, monoids and semirings. At present, I am studying and developing notions of some important classes of morphisms for monoid schemes. I am also interested in the applications of F1-geometry in toric and tropical geometry, which has been of much interest in recent times. 

Here is a link to the recorded lectures from the ongoing online seminar THE F1 WORLD SEMINAR organized by Jaiung Jun, Oliver Lorscheid, Yuri Manin, Matt Szczesny, Koen Thas and Matt Young. Lectures from this seminar revolves around F1 and its several connections to different areas in mathematics such as arithmetic, geometry, representation theory and combinatorics.