# Online Seminar of Assamese Mathematicians

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This seminar takes place usually on Fridays, at a suitable time and is meant for talks by young Assamese mathematicians (PhD Students, Postdocs, and young faculty members). By Assamese, we mean anyone residing/working in Assam now or residing/working in Assam in the past. If you wish to attend or give a talk in the seminar please email me ([email protected]) or Parama Dutta ([email protected]).

Check the FAQs.

All the talks will be over Zoom and the meeting details will be emailed to the registered participants.

## Next Talk

Congruences for $\ell$-Regular OverPartition for $\ell\in {5, 6, 8}$

Chayanika Boruah (University of Science and Technology, Meghalaya)

16 October 2020 (8 pm IST)

Abstract: A partition of a positive integer $n$ is a non-increasing sequence of positive integers, called parts, whose sum equals $n$. For any positive integer ${\ell}$, ${\ell}$-regular partition of a positive integer $n$ is a partition of $n$ such that none of its part is divisible by ${\ell}$. An overpartition of a positive integer $n$ is a partition of $n$ in which the first occurrence of each part can be over lined. Let $\bar{A}^\ell(n)$ denote the number of overpartitions of a non-negative integer $n$ with no part divisible by $\ell$, where $\ell$ is a positive integer. We prove, infinite family of congruences for $\bar{A}^5(n)$ modulo 4, $\bar{A}^6(n)$ modulo 3, and $\bar{A}^8(n)$ modulo 4. We also prove some other congruences.

## Upcoming Talks

Please click on the title to see the abstract.

30 October, 2020: tba (Kunjakanan Nath, Université de Montréal, Canada) tba
06 November, 2020: On Congruent Numbers and Their Generalizations over Number Fields (Shamik Das, Indian Institute of Technology Guwahati) A natural number n is called a congruent number if it is the area of a right triangle with rational lengths. The classical problem of determining whether a given natural number is congruent or not is known as the congruent number problem which still remains unsolved. Here we mainly discuss two aspects of congruent number briefly. Firstly, construction of in finitely many new families, each containing infinitely many non-congruent numbers and secondly, a criterion for a natural number to be theta-congruent over certain real number fields, where theta-congruent numbers is a generalization of congruent numbers where one considers triangles with an angle theta such that cos theta is a rational number.
20 November, 2020: Introduction to the mapping class groups (Soumya Dey, The Institute of Mathematical Sciences (IMSc), Chennai) We shall discuss basic notions and fundamental results in the theory of mapping class groups of surfaces. Prerequisite for the talk would be undergraduate courses on topology and group theory.
27 November, 2020: An introduction to combinatorial representation theory (Manjil Saikia, Cardiff University) We will give a leisurely introduction to combinatorial representation theory, focusing mainly on the symmetric group. The talk will be self-contained and only basic knowledge of abstract and linear algebra will be assumed.
04 December, 2020: tba (tba) tba
11 December, 2020: tba (tba) tba
18 December, 2020: tba (tba) tba

## Past Talks

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)

## 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, but you have to register to get the links to attend the seminars. You can register by sending an email to [email protected], mentioning your name and affiliation (if any).

Who can give a talk?

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

Will there be any certificate for attending?

No.