Prior to joining IIT Palakkad, Dr. Kumar was a Postdoctoral Fellow at New Mexico State University, USA (August 2023–July 2026), where he combined research with undergraduate and graduate teaching, student mentoring, and seminar organization. Earlier, he held postdoctoral positions at the Chennai Mathematical Institute (March 2021–July 2023) and IIT Delhi (September 2020–February 2021), following a Pre-Postdoctoral Fellowship at IIT Madras (March–August 2020). His postdoctoral research in India was supported by the National Postdoctoral Fellowship. 

Dr. Kumar earned his Ph.D. in Mathematics from IIT Madras in 2020 under the supervision of Prof. A. V. Jayanthan, with a thesis entitled Homological Properties of Binomial Edge Ideals. IIT Madras recognized his doctoral research with the Institute Research Award for outstanding and creative research and the Smt. Lakshmikutty Amma and Shri A. Krishnankutty Nair Prize for the Best Ph.D. Thesis in Mathematics. He received his M.Sc. in Mathematics from IIT Madras (2016) and B.Sc. (Hons.) in Mathematics from the University of Delhi (2014). His undergraduate and master's studies were supported by the DST INSPIRE Scholarship, while his doctoral studies were supported by the NBHM Doctoral Fellowship. 

Student research and mentoring are an important part of his academic interests. At New Mexico State University, Dr. Kumar initiated and led the department's first summer research program, mentoring an undergraduate and a graduate student on a project that resulted in a joint publication in the Journal of Algebraic Combinatorics. He is particularly interested in developing research projects that enable students to begin with concrete algebraic and combinatorial problems and progress toward deeper structural questions.