Rajan did his MSc (Integrated) from IIT Kanpur. Subsequently he joined TIFR as a graduate student and continued as a faculty member till the end of 2021. He has held visiting scientist positions at McGill University, Max Planck Institut fur Mathematik and Institute for Advanced Study.
He is a fellow of the Indian Academy of Sciences and the Indian National Science Academy. He is an editor in Indian Journal of Pure and Applied Mathematics, Journal of Algebra and its Applications and is the Chief Editor for Proceedings of the Mathematical Sciences of the Indian Academy of Sciences.
His mathematical interests are centred around number theory, arithmetic geometry, automorphic forms and representation theory.