# Seminars

Online Weekly Research Seminar for Early Career Mathematicians from India.

This seminar takes place usually on Fridays, at a suitable time and is meant for talks by early career Indian mathematicians (PhD Students, Postdocs, and young faculty members). By Indian, we mean anyone residing/working in India now or residing/working in India in the past.

You can register to be on the mailing list by filling in this form. Alternatively, you can also email me ([email protected]) or Parama Dutta ([email protected]).

Check the FAQs.

All the talks will be over Zoom. To join a talk please use the following information: Meeting ID 926 1140 2828 and the Passcode is 1729.

## Next Talk

Combinatorial proof of a beautiful Euler-type Identity

Gauranga K. Baishya (Tezpur University)

26 February 2021 (7 pm IST)

Abstract: Let a(n) be the number of partitions of n such that the set of even parts have exactly one element, b(n) be the difference between the number of parts in all odd partitions of n and the number of parts in all distinct partitions of n and c(n) are the number of partitions of n in which exactly one part is repeated. One can show that a(n)=b(n) and b(n)=c(n) separately. We will prove combinatorially, the beautiful identity that a(n)=b(n)=c(n). The proof relies on bijections between a set and a multiset, where the partitions in the multiset are decorated with bit strings. This is an expository talk.

## Upcoming Talks

• 05 March, 2021: to be announced (Mohan Swaminathan, Princeton University, USA)
• 12 March, 2021: Parametrized Families of Quadratic Fields with Large n-rank (Azizul Hoque, Rangapara College, Assam)
• 19 March, 2021: to be announced (Tushar Kanta Naik, Indian Institute of Science Education and Research, Mohali)
• 26 March, 2021: to be announced (Gianluca Faraco, Indian Institute of Science, Bengaluru)
• 09 April, 2021: to be announced (Bidisha Roy, Polish Academy of Sciences, Warsaw, Poland)
• 23 April, 2021: to be announced (Diksha Tiwari, Universität Wien, Austria)
• 30 April, 2021: to be announced (Uday Bhaskar Sharma, Tata Institute of Fundamental Research, Mumbai)
• 07 May, 2021: to be announced (Soumya Dey, The Institute of Mathematical Sciences, Chennai)
• 14 May, 2021: to be announced (Eshita Mazumdar, Indian Statistical Institute, Bengaluru)
• 21 May, 2021: to be announced (to be announced)
• 28 May, 2021: Plane Partitions and Other Topics (Subhajit Bandyopadhyay, Tezpur University)

## Past Talks

Click on the title to view the slides (if they are available).

1. What is the Probability that an automorphism fixes a group element? (Parama Dutta: 26 June 2020)
2. Hypergeometric Series over Finite Fields (Arjun Singh Chetry: 10 July 2020)
3. Families of Congruences for Fractional Partition Functions Modulo Powers of Primes (Hirakjyoti Das: 17 July 2020)
4. Combinatorics of Stammering Tableaux (Bishal Deb: 31 July 2020)
5. An approach to construct Mathematical model through system of ordinary differential equation (Munmi Saikia: 07 August 2020)
6. Some aspects of $\Gamma_2$ graph over some of the finite commutative rings (Anurag Baruah: 14 August 2020)
7. Application of the Rogers-Ramanujan continued fraction to partition functions (Nilufar Mana Begum: 21 August 2020)
8. Certain types of primitive and normal elements over finite fields (Himangshu Hazarika: 28 August 2020)
9. Hard and Easy Instances of L-Tromino Tilings (Manjil Saikia: 04 September 2020)
10. Extremal inverse eigenvalue problems for matrices with a prescribed graph (Debashish Sharma: 18 September 2020)
11. Solution Concepts in Transferable Utility Games (Parishmita Baruah: 02 October 2020)
12. Distance Pareto eigenvalue of a graph (Deepak Sarma: 09 October 2020)
13. Congruences for $\ell$-Regular OverPartition for $\ell\in {5, 6, 8}$ (Chayanika Boruah: 16 October 2020)
14. Primes with restricted digits in arithmetic progressions (Kunjakanan Nath: 30 October 2020)
15. On Congruent Numbers and Their Generalizations over Number Fields (Shamik Das: 06 November 2020)
16. Introduction to the mapping class groups (Soumya Dey: 20 November 2020)
17. An introduction to combinatorial representation theory (Manjil Saikia: 27 November 2020)
18. $\mu$-Statistically Convergent Multiple Sequences in Probabilistic Normed Spaces (Rupam Haloi: 04 December 2020)
19. On the parity of Andrews’ Singular overpartition function (Ajit Singh: 11 December 2020)
20. The Stable Marriage Problem: Marriages made by algorithms, Guaranteed with stability! (Souvik Parial: 18 December 2020)
21. Generalization of five $q$-series identities of Ramanujan and unexplored weighted partition identities (Bibekananda Maji: 08 January 2021)
22. Interconnected sequences: A generalization of Fibonacci sequence and some identities (Neeraj Kumar Paul: 22 January 2021)
23. Tessellation by Equilateral Polygons (Anirban Roy: 29 January 2021)
24. Enumeration of matrices and splitting subspaces over finite fields (Divya Aggarwal: 12 February 2021)
25. Voting Rules: An Introduction (Ritu Dutta: 19 February 2021)

## FAQs

When does the seminar take place?

Usually on Fridays, the times change depending on the availability of the speaker.

Who can attend?

Everyone is welcome to attend. You can register to be on the mailing list by filling in this form.

Who can give a talk?

At the moment we are encouraging only PhD students, postdocs and young faculty members to give talks. If you are interested in giving a talk, please send an email to [email protected] or [email protected]

Are the talks meant for a general audience?

Yes, but this is a research seminar. We ask the speakers to spend at least 30% of their time on introduction and motivation of the topic which should be understandable for someone with a Masters level education in mathematics.

How long is a talk?

The talks are between 45-60 minutes, followed by discussions. We leave the discussions open ended and usually spend about 60 minutes after the talk just chatting with each other about various topics related to mathematics.