## Sunday, March 15, 2020

### Cancellations etc.

March 14, 2020 (Pie Day!)

Dear all,

I am sorry to inform you that as per JNU administration requirements, no meetings are allowed. So we have decided to postpone the seminars to April. In case the situation permits in April, I hope we will meet every week and pursue our agenda.

The agenda, which got clarified since my previous email, is as follows:

a. Circle Method by Manoj Verma
b. Intersection Numbers using Yang-Mills Theory on Riemann Surfaces, by Debashis Ghoshal
c. Mini Course on Continued Fractions 1: Basic Moves by Gaurav Bhatnagar
d. Mini Course on Continued Fractions 2: Convergence Theorems by Krishnan Rajkumar

Meanwhile, this is a wonderful opportunity to stay quarantined, not meet anyone, and focus all our efforts on our research for a couple of weeks! I suppose I should have said "I am happy to inform you..."

Best wishes,

Gaurav Bhatnagar and Krishnan Rajkumar

March 11, 2020

Dear all,

We hope you had a safe and happy holi. The last couple of months of the academic year are upon us, and we thought we will do something special before we close for the summer.

The next talk in our Topics in Special Functions and Combinatorics Seminar is on March 17, 2020. It is by Manoj Verma and it is on Waring's problem and the circle method. The abstract appears below.

The talk after that is by Debashis Ghoshal on March 31.

In April, there will be 2-4 talks on the topic of Continued fractions by the two organizers of this seminar. These talks will comprise a mini-course on the subject of continued fractions. We plan to cover the basic moves as well as the convergence theory. Since this topic is not covered in most graduate courses, we hope this will be something unique and useful, especially for those with interests in Combinatorics, Number Theory and Special Functions. We will come back with details soon; please keep your tuesday afternoons free if you are interested, and kindly let interested students know about this.

In all of the above, the lecturers have promised a focus on techniques and will provide (optional) exercises, so that those of us who are interested can actually get our hands dirty and learn something which we can use in our work.

Best wishes,

Krishnan Rajkumar  and Gaurav Bhatnagar

TALK ANNOUNCEMENT

Speaker: Manoj Verma (SPS, JNU)

Title: Waring's problem and the circle method

When: Tuesday, March 17, 2020, 4 pm.

Where: Seminar Room, School of Physical Sciences (SPS), Dr. CV Raman Marg, JNU.
(TO BE CONFIRMED)

Abstract: This talk will be an introduction to the circle method for those with no previous familiarity with the circle method. I shall introduce the method using Waring's problem as the prototype. For a positive integer $k$, let $G(k)$ denote the smallest positive integer $s$ such that every sufficiently large positive integer is a sum of s kth powers of integers. We shall sketch a proof of the fact that $G(k)$ is less than or equal to $2^{k} + 1$.

Students are welcome.