Shanta Laishram, ISI, Delhi Center

Title: Binary Recurrence Sequences and its Arithmetic

Where: Conference Room, School of Physical Sciences (SPS)

Speaker: Shanta Laishram, Indian Statistical Institute, Delhi

Abstract: 

The Fibonacci sequence, which is one of the most well known integer sequences, is a special example of a general family of Binary recurrence sequences. In this talk, I will present an overview of Binary recurrence sequences, their interesting properties and arithmetic. Some well known open problems in the areas will also be highlighted.

Shanta Laishram, Conference Room, School of Physical Sciences, JNU (Dec 2019) 

Here is a link to his presentation.

Krishnan Rajkumar, SC&SS, JNU

Title: Apery's theorem and a continued fraction of Ramanujan

Speaker: Krishnan Rajkumar, SC&SS, JNU

Where: Room 111, School of Physical Sciences (SPS)

Abstract:

We will discuss Apéry's "miraculous" proof of the irrationality of ζ(3) as well as the claim that Apéry's constructions were motivated from a "table" of Ramanujan. We will then present a method of deriving certain continued fractions in Ramanujan's notebooks that also provides a proof of Apéry's theorem.

Gaurav Bhatnagar, SPS, JNU

Title: How to discover the Rogers-Ramanujan identities
Speaker: Gaurav Bhatnagar, SPS, JNU


Where: Seminar Room, School of Physical Sciences (SPS)

Abstract:
The Rogers-Ramanujan identities were sent by Ramanujan to Hardy in a letter more than a 100 years ago. In the next few years, the identities were circulated among mathematicians, but nobody, including Ramanujan, could prove them. Then one day, while riffling through old back copies of the journal, Ramanujan discovered them in an obscure paper written in 1894 by the English mathematician Rogers. Later, these identities were discovered independently by Schur in a combinatorial context, and then again in 1980 by Baxter in the context of mathematical physics.  We don’t know how Ramanujan got to them, but we examine a method to conjecture these identities which Askey has suggested may be the way Ramanujan discovered them.   

Announcing the SF and NT Seminar

We are organizing a seminar on topics in Special Functions and  Number Theory. The meetings will  be held in the School of Physical Sciences, CV Raman Marg in the JNU Campus. At present we plan to meet approximately every other week, on Tuesdays at 3:45 pm.  We would like to discuss problems of mutual interest, and to learn techniques that can be used by us in our own problems. Regular participants are expected to contribute by speaking on their own research, or someone else's research, but of interest to them. 

Graduate students are welcome. In case you are interested in getting notifications of talks, please let Gaurav Bhatnagar or Krishnan Rajkumar  know.  If you know people who may be interested, please feel free to let them know.