I am Mohammad Ashraf Bhat, a Ph.D. student in the Department of Mathematics at the Indian Institute of Technology Ropar, under the supervision of Dr. G. Sankara Raju Kosuru (Associate Professor, IIT Ropar). I am a recipient of the Prime Minister’s Research Fellowship (PMRF), awarded through the 7th cycle (May 2021).

My research focuses on Functional Analysis, Metric Measure Spaces, and the theory of Function Spaces. I have worked on Sobolev spaces over metric spaces, particularly studying the pointwise properties of Sobolev functions and measure-theoretic aspects. Another part of my work involves Köthe amalgam spaces, exploring infinite direct sum structures within Banach and quasi-Banach settings. I have also contributed to the theory of rearrangements of functions, with applications to concentration inequalities in probability.

Broadly, my research brings together techniques from measure theory, functional analysis, and potential theory, aiming at a deeper understanding of analytic structures in both classical and modern frameworks