Room 004, School of Arts and Sciences
Central Campus
Classical hypergeometric series are a generalisation of geometric series, wherein the ratios of consecutive terms are now rational functions, rather than constants. (They also appear very naturally from Gauss' hypergeometric differential equation.) Greene introduced an analogous notion of hypergeometric series on finite fields, which has given rise to a lot of recent work in the area. We will introduce all these concepts and also p-adic analogues of hypergeometric series and mention some of our results in this area. This talk will not assume a lot of background and we will introduce most of the notions as we move along.
Professor Rupam Barman is a Number Theorist working in the Indian Institute of Technology (IIT) Guwahati since 2016. Prior to joining IIT Guwahati he has held positions at IIT Delhi and Tezpur University. His research is in Algebraic Number Theory, Elliptic Curves, Iwasawa Theory, Modular Forms, and the Theory of Partitions, among other subjects. For his research, he was awarded the A M Mathai Research Excellence Award in 2022 by the Society for Special Functions and their Applications. At present, he is an editor of The Ramanujan Journal.
