Room 201, School of Arts and Sciences
Central Campus
The Rogers--Ramanujan identities are two identities discovered by Ramanujan and sent to Hardy in a letter. For a while, no-one, including Hardy and Ramanujan could prove them. Then Ramanujan found them while riffling through an old paper of Rogers.
We will show how to prove these identities using a technique called the Bailey Transform and Lemma. This technique is linked to a technique that can be used to solve the following problem: If $n$ letters are placed randomly in $n$ previously addressed envelopes, what is the probability that no letter reaches the right person?
Gaurav Bhatnagar obtained his PhD in Mathematics from The Ohio State University in 1995. After his PhD, he spent one year each at Ohio State and the Indian Statistical Institute, Delhi. Subsequently, he joined the educational technology industry, where he has been able to make a significant contribution to the teaching and learning processes of Indian schools. Since September 2015, he has been a post-doctoral researcher or visiting faculty in various institutions, including ISI, Delhi; the Faculty of Mathematics at the University of Vienna; the School of Physical Sciences (SPS), JNU; and Ashoka University.
He has co-edited (with Sugata Mitra and Shikha Mehta) An Introduction to Multimedia Systems (Academic Press, 2002). He has written Get Smart: Maths Concepts (Penguin, 2008), a book on middle school mathematics; a Puzzle book (with Tejasi Bhatnagar): Maths Puzzles for Smart Kids (Hachette, 2023). His latest book is Experience Mathematics (Hem Aunty Publications, 2025).
His research interests are in Combinatorics and Special Functions, more specifically, hypergeometric, q-hypergeometric, and elliptic hypergeometric series, their multiple series extensions over root systems, continued fractions, orthogonal polynomials, partitions and elementary number theory. He is also interested in providing a discovery approach to Ramanujan’s identities.
