## Tuesday, January 28, 2020

### Yash Lodha, EPFL, Lausanne

Title: The von Neumann-Day problem for finitely presented groups.

Speaker: Yash Lodha, EPFL, Lausanne
Where: Seminar Room, School of Physical Sciences (SPS), C V Raman Marg, JNU
When: Tuesday, January 28, 2020, 4 PM

Abstract:

The so called von Neumann-Day problem asks if there exist nonamenable groups that do not contain nonabelian free subgroups. I will describe a recent solution to the problem for the class of torsion free finitely presented groups (joint with Justin Moore). The groups emerge as groups of homeomorphisms of the real line, and an encoding by means of continued fractions is used to prescribe a certain combinatorial structure. This structure allows us to establish that the groups are finitely presented.

## Wednesday, January 8, 2020

### Gaurav Bhatnagar, SPS, JNU

Title: Ramanujan's $q$-continued fractions
Speaker: Gaurav Bhatnagar
When: Tuesday, January 14, 2020; 4:00--5:00 pm,
Where: Seminar Room, Indian Statistical Center, 7 SJS Sansanwal Marg, Delhi 110016

ABSTRACT

It is exactly a hundred years since Ramanujan died at an early age of 32 years, but his mathematical legacy lives on. One of the things he was famous for was his work on continued fractions. We will give a brief introduction to Ramanujan's life and the material available on his story and his work. We will show Ramanujan's $q$-continued fractions and show how an elementary idea used by Euler can be used to prove many of Ramanujan's continued fractions. We expect to briefly mention some topics of current research interest. Students are welcome; much of the talk will be suitable for a general audience.

***

 A page from Ramanujan's Lost Notebook with some continued fractions

## Wednesday, January 1, 2020

### Special Functions and Number Theory: About Us

It was a long, hard, grim winter. I was working a sixty-hour week at Bomber Command. The bomber losses which I was supposed to analyze were growing steadily higher. The end of the war was not in sight. In the evenings of that winter I kept myself sane by wandering in Ramanujan's garden, reading the letters I was receiving from Bailey, working through Bailey's ideas and discovering new Rogers--Ramanujan identities of my own.
This was written by Freeman J. Dyson in his paper celebrating the centenary of Ramanujan's birth. This year, 2020, is the centenary of Ramanujan's passing. So our first talk of the year is on Ramanujan and some of his work. Students are welcome.

We hope this year our seminar will thrive and build on what we have just begun. In addition, we hope we will get an opportunity to listen to the next generation of budding mathematicians in topics related to special functions and number theory.

We wish you a happy and productive 2020, with many new ideas and papers.

Gaurav Bhatnagar and Krishnan Rajkumar

2020: New Year Message

UPDATE (4 June 2020):

This was a new year message we wrote a few months ago, before a talk was held in ISI, Delhi (rather than JNU). But it seems appropriate for the year we are going through. The seminar was stopped for a few months due to a lockdown. Now we are starting again, with an expanded agenda.

Atul Dixit has joined as a co-organiser and we hope to make this seminar an international group. However, at present, we wish to keep timings as per our our Indian schedule, so as not to lose focus on those whom we wish to benefit the most. However, we will on occasion change timings to suit our international speakers.

The above quote is an appropriate one for many reasons. If you scan through the talks in this seminar, Ramanujan's mathematics plays a large role in almost all of them. This also represents the three organizer's own interests.

Finally, a word on what we request of speakers. We would like to learn techniques which we can use in our own problems; and sometimes learn about problems which we can solve using our techniques. Many students and people with a variety of  interests come for the talks, so make sure you have something everyone can take home.

June 4, 2020
Gaurav Bhatnagar, Atul Dixit and Krishnan Rajkumar