Research Interests:-
My research interest lies in Algebraic and Arithmetic Geometry. More specifically, I am interested in Differential Algebra, Arithmetic Jet Spaces, and Delta Geometry.
Please find a copy of my Thesis here.
Brief Description:-
Similar to the construction of real numbers, for each rational prime p, one can introduce a number system known as p-adic numbers, which encodes several arithmetic information that real or complex numbers can not. The usual differentiation no longer survives over p-adic numbers, prompting a search for a differentiation analog that could function within this arithmetic context. Based on a prior work of A. Joyal, A. Buium introduced the notion of p-derivation denoted as δ to derive arithmetic applications analogous to the theory of functions in differential algebra. This construction marked the beginning of delta geometry, which seeks to translate differential concepts into the p-adic domain, connecting number theory with geometric intuition.
In my recent research work with my supervisor Prof. Arnab Saha, we constructed a generalized version of the delta-cocrystals introduced by J. Borger and A. Saha earlier. These generalized delta-isocrystals reveal intriguing Hodge-theoretic properties, opening up new directions for understanding their structure and applications.