# 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

Solution Concepts in Transferable Utility Games

Parishmita Baruah (Dibrugarh University)

02 October 2020 (8 pm IST)

Abstract: In cooperative games with transferable utility (TU games in short), players work together for a common goal under binding agreements. The contributions by the players to achieve this common goal fetch them some worth. But one question naturally arises, how fair is the distribution of total worth generated due to their cooperation among the players? As a result, many solution concepts have been put forward over the years. By defining so-called solution concepts, cooperative game theory tries to characterize the set of outcomes that are, seen from a viewpoint of rationality, interesting. In the most general setup of TU games, the players’ contributions cannot be directly determined and, therefore, are measured indirectly by a term called “marginal contributions”. Thus, the notion of marginal contribution is an indicator of the productivity of a player. The designer may or may not consider a player’s productivity as a preferable criterion for her solution. This leads to the definition of two extreme classes of solutions: the class of marginalistic solutions and the egalitarian solutions. The marginalistic solutions award players according to their productivities, whereas the egalitarian solutions express solidarity to the non-productive players. This work will discuss some solution concepts of TU-games that behave as a trade-off between marginalism and egalitarianism and their corresponding axiomatic characterizations.

## Upcoming Talks

Please click on the title to see the abstract.

09 October, 2020: tba (Deepak Sarma, Assam Agricultural University, Jorhat) tba
16 October, 2020: Congruences for $\ell$-Regular OverPartition for $\ell\in \{5, 6, 8\}$ (Chayanika Boruah, University of Science and Technology Meghalaya) 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.
30 October, 2020: tba (Kunjakanan Nath, Université de Montréal, Canada) tba
06 November, 2020: tba (Shamik Das, Indian Institute of Technology Guwahati) tba
20 November, 2020: tba (tba) tba
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.

## 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)

## 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.