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.

**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.

*Please click on the title to see the abstract.*

**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)

**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.