Ramanujan Explained - Lecture 2 - May 2, 2024, 4:00 PM- 5:00 PM IST

 Dear all,

The second talk in the Ramanujan Explained course will be on the q-binomial theorem. There is now a website https://ramanujanexplained.org which contains (draft) lecture notes as well as a link to the video of the first lecture. In addition, there is a video link for visitors located in China (courtesy Shishuo Fu).

Talk Announcement: 

Title:  Ramanujan Explained 2: The $q$-binomial theorem

Speaker:  Gaurav Bhatnagar (Ashoka University)
When: May 2, 2024, 4:00 PM- 5:00 PM IST 

Where: Please ask the organisers for the link

Live LInk: https://youtube.com/live/bppF_WXPmVU?feature=share

Abstract:

We begin our study of Ramanujan's identities. The Rogers-Ramanujan identities appear Chapter 16 of Volume 3 of Berndt's Ramanujan's notebooks. One of the key results there is the q-binomial theorem. We will begin with a discovery approach to the binomial theorem and then give Ramanujan's own proof of the q-binomial theorem. Ramanujan developed hypergeometric series in an earlier chapter, so chances are that he was motivated to find a more general series with an additional parameter. 

Ramanujan Explained - Lecture 1 - April 18, 2024, 4:00 PM- 5:00 PM IST

 Dear all,

We are launching a course under the title of Ramanujan Explained. There will be a series of lectures, all given by Gaurav Bhatnagar, with accompanying notes and exercises. The goal is to cover (a large number of) Ramanujan's identities. The first talk in this series is in our next seminar slot. Kindly do share this announcement with students who may be interested in Ramanujan and his mathematics. The first few lectures will target $q$-hypergeometric series and special cases, and can serve as an introduction to basic hypergeometric series. We hope these lectures will serve as a useful supplement to the monumental work of Bruce Berndt  (Ramanujan's Notebooks I-V) and George Andrews and Bruce Berndt  (Ramanujan's Lost Notebook I-V).  

Lecture notes, slides and more: Ramanujan Explained Website

Talk Announcement: 

Title:  Ramanujan Explained 1: How to discover the Rogers-Ramanujan identities

Speaker:  Gaurav Bhatnagar (Ashoka University)
When: April 18, 2024, 4:00 PM- 5:00 PM IST 

Where: Zoom: Write to the organisers (sfandnt at gmail dot com) for the link

Live LInk: https://youtube.com/live/_M4WbbAffIA?feature=share

Abstract:

About the Rogers-Ramanujan identities, Hardy famously remarked: "It would be difficult to find more beautiful formulae than the "Rogers-Ramanujan" identities... " In the first introductory lecture in the Ramanujan Explained course, we explain Askey's idea on how Ramanujan may have come across these identities. Continued fractions played an important part of Ramanujan's work, and Askey's explanation is all about the simplest $q$-continued fraction and how it naturally leads to the Rogers-Ramanujan identities.