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

**A Stroll Through Davenport Constant**

**Eshita Mazumdar (Indian Statistical Institute, Bengaluru)**

**21 May 2021 (7 pm IST)**

**Abstract**: For a finite abelian group G, the Davenport Constant D(G) is defined to be the least positive integer k such that any sequence S with length k over G has a non-trivial zerosum subsequence. The original motivation for introducing Davenport Constant was to study the problem of non-unique factorization domain over number fields. The precise value of this group invariant for any finite abelian group is still unknown. In my talk I am going to present my most recent research works related to Davenport Constant. In first half of my talk, I will present an Extremal Problem related to Weighted Davenport Constant, where we introduce and discuss several exciting combinatorial results for finite abelian group. In second half of my talk, I will talk about my current project, where my main aim is to discuss the perfect power of a polynomial $f(x)\in \mathbb{Z}[x]$ for integral values of x: While doing so we developed a new group invariant whichis a natural generalization of Davenport Constant.

**28 May, 2021**: Extended higher Herglotz functions I. Functional equations (**Rahul Kumar**,*Indian Institute of Technology Gandhinagar*)

*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)**Combinatorial proof of a beautiful Euler-type Identity**(*Gauranga K. Baishya*: 26 February 2021)**Gromovâ€™s compactness theorem for (pseudo)holomorphic curves**(*Mohan Swaminathan*: 05 March 2021)**Parametrized Families of Quadratic Fields with Large n-rank**(*Azizul Hoque*: 12 March 2021)**Finite Groups with Exactly Two Conjugacy Class Size and the Analogous Study in Lie Algebra**(*Tushar Kanta Naik*: 19 March 2021)**Translation surfaces with poles and meromorphic differentials**(*Gianluca Faraco*: 26 March 2021)**On some properties of consecutive Lehmer numbers modulo a prime**(*Bidisha Roy*: 09 April 2021)**Commuting Tuples and Commuting Probability**(*Uday Bhaskar Sharma*: 30 April 2021)**Orbits of zipping maps of surfaces of infinite type**(*Soumya Dey*: 07 May 2021)**Simultaneous divisibility and indivisibility properties of class numbers of quadratic fields**(*Jaitra Chattopadhyay*: 14 May 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.