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

**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.

**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**,*UniversitĂ¤t 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)

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

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

**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.

**Why was this series started?**

The primary aim was to know the different type of work being done by young mathematicians and to also look for oppurtunities for collaborative work.

**Will there be any certificate for attending?**

No.

**Are there recordings of the talks?**

No. Only the speaker has access to recordings of their own talks. The speakers can decide to make them public if they wish to.