Speaker: Dr. Lalit Vaishya, DST-INSPIRE FACULTY, Indian Statistical Institute, New Delhi.
Title: Riemann zeta function: Basics and distributions of its zeros, and Current progress.
Date and time: 12 September 2025, Friday.
Time and Venue: 5:00 PM to 6:00 pm, Online ( https://meet.google.com/gea-oazf-rqx )
Abstract: The Riemann zeta function ζ(s) plays a fundamental role in number theory, especially in understanding the distribution of prime numbers. it extends analytically to the complex plane and satisfies a nice functional equation. The Riemann Hypothesis predicts the location of zeros in the critical strip. Precisely, it conjectured that all the non-trivial zeros of ζ(s) lie on the critical line Re(s)=1/2.
Hardy (1914) proved that there are infinitely many zeros on the critical line. Modern advances from random matrix theory and spectral methods describe zero-density and spacing. A similar result has been predicted for the automorphic L-functions. We will give a brief survey in this direction.
Speaker: Tushar Karmakar (Tulane University, USA)
Title: Theta Series and Representation of Integers as a sum of squares.
Date and time: 29 August 2025, Friday
Time and Venue: 5:00 PM to 6:00 pm, Online (https://meet.google.com/svz-prhd-ypr)
Abstract: Theta series arise naturally in mathematics as generating functions that encode arithmetic information, and they also carry rich connections to modular forms. In this talk, we will introduce the basic ideas behind theta series and modular forms of half-integral weight. As a main application, we will see how these ideas lead to an elegant proof of Lagrange’s Four-Square Theorem, which states that every positive integer can be written as a sum of four squares.
Speaker: Rohit Yadav
Title: Toward the nonexistence of odd Perfect Numbers.
Date and time: 22 August 2025, Friday
Time and Venue: 5:00 PM to 6:00 pm, 01- AC-207
Abstract: In this talk, I will discuss a recursively defined integer sequence conjectured to reach $1$ for every positive starting value. Although similar in spirit to the Collatz conjecture, this problem has distinct structural features. Interestingly, its resolution would also prove that odd perfect numbers cannot exist, a question that has remained open for centuries. I will present a set of integers for which the sequence can be shown to reach $1$, providing partial support for the conjecture.
This is joint work with Ritesh Dwivedi.
Speaker: Prabhat Kumar Mishra
Title: Bruhat Tits spaces.
Date and time: 25 April 2025, Friday
Time and Venue: 5:00 PM to 6:00 pm, 01- AC-207
Abstract: Bruhat Tits spaces are complete metric spaces which satisfy semi parallelogram law. In this talk, we will discuss these spaces and some of the examples. We will also see Bruhat Tits fixed point theorem.
Speaker: Hridesh Kumar
Title: Bivariate local permutation polynomials and their relation with Latin squares. (Part I)
Date and time: 18 April 2025, Friday (Part II)
Time and Venue: 5:00 PM to 6:00 pm, 01- AC-207
Abstract: In this talk, we introduce the concept of bivariate local permutation polynomials over the finite field $\F_q$. We also study their relation with Latin squares of prime power order $q$. Finally, we will discuss a recently developed technique that offers new insights into the study of bivariate local permutation polynomials.
Speaker: Rohit Yadav
Title: Euler’s Formula and the Classification of Regular Polyhedra.
Date and time: 11 April 2025, Friday
Time and Venue: 5:00 PM to 6:00 pm, 01- AC-207
Abstract: Euler’s formula provides a powerful numerical relationship arising from a geometric-topological setting: for any finite graph G that can be drawn in the plane or on a sphere, the numbers of vertices 𝑛, edges 𝑒, and faces 𝑓 satisfy the relation 𝑛 − 𝑒 + 𝑓 = 2. Many classical results follow from Euler’s formula, including the classification of the regular convex polyhedra. In this talk, we will present an elementary proof of Euler’s formula and explore some of its applications.
Speaker: Hridesh Kumar
Title: Bivariate local permutation polynomials and their relation with Latin squares. (Part I)
Date and time: 04 April 2025, Friday (Part I)
Time and Venue: 5:00 PM to 6:00 pm, 01- AC-207
Abstract: In this talk, we introduce the concept of bivariate local permutation polynomials over the finite field $\F_q$. We also study their relation with Latin squares of prime power order $q$. Finally, we will discuss a recently developed technique that offers new insights into the study of bivariate local permutation polynomials.
Speaker: Sonakshee Arora
Title: From Young Tableaux to Representations of the Symmetric Group
Date and time: 21 March 2025, Friday
Time and Venue: 5:00 PM to 6:00 pm, 01- AC-207
Abstract: The symmetric group plays a fundamental role in combinatorics, algebra, and physics, with its irreducible representations providing deep insights into the structure of permutations. In this talk, we introduce the representation theory of Symmetric group using the combinatorial framework of Young tableaux.
Speaker: Muskan Khaneja
Title: A Gentle Introduction to Young Tableaux.
Date and time: 07 March 2025, Friday
Time and Venue: 5:00 PM to 6:15 pm, 01- AC-207
Abstract: Young tableau is a combinatorial object that has vital applications in algebra of symmetric functions, the representations of the symmetric and general linear groups, and the geometry of flag varieties. In this talk, we will understand this object from scratch and see some of its basic properties.
Speaker: Mukul Dwivedi
Title: Integration in 𝑅^n : Fundamentals and Intuition.
Date and time: 21 February 2025, Friday
Time and Venue: 5:00 PM to 6:15 pm, 01- AC-207
Abstract: In this talk, I will discuss the very basic aspects of integration on R^n, the fundamental theorem of calculus, and Fubini’s theorem. The focus will be on their intuitive understanding and fundamental applications.
Speaker: Dr. Chandan Kumar Vishwakarma
Title: Permutation Polynomials over Finite Fields.
Date and time: 14 February 2025, Friday
Time and Venue: 5:00 PM to 6:15 pm, 01- AC-207
Abstract: A polynomial f(x) in F_q [x] is a permutation polynomial of F_q if its associated polynomial function f : c → f(c) from F_q to itself is a permutation of F_q. In this talk, we will explore an application of permutation polynomials over finite fields to partition theory.
Speaker: Dr. Bijender
Title: From Hypergraphs to Vertex-Decomposable Structures.
Date and time: 07 February 2025, Friday
Time and Venue: 5:00 PM to 6:15 pm, 01- AC-207
Abstract: We discuss the notion of vertex-decomposable hypergraphs and present a method for constructing a vertex-decomposable hypergraph from a given hypergraph.
Speaker: Prabhat Kumar Mishra
Title: An invitation to p-adic world.
Date and time: 31 January 2025, Friday
Time and Venue: 5:00 PM to 6:15 pm, 01- AC-207
Abstract: The p-adic numbers introduced by Kurt Hensel in 1897 have become ubiquitous in modern number theory. These possess many fascinating and unconventional properties that set them apart from the real numbers, offering deep insights into arithmetic and algebraic structures. In this talk, we will understand the step-by-step construction of p-adic numbers, starting from their foundational ideas, and explore some of their key arithmetic properties. We will discuss how they provide a fresh perspective on solving problems in number theory.
Note: This talk is accessible to everyone; no prior background knowledge is required.
Speaker: Rohit Yadav
Title: K-Nullstellensatz for arbitrary fields.
Date and time: 23 January 2025, Thursday
Time and Venue: 5:00 PM to 6:15 pm, 01- AC-207
Abstract: Hilbert's Nullstellensatz, established in 1893, is a foundational result in algebraic geometry. Originally formulated for algebraically closed fields, Terjanian introduced a corresponding version for finite fields in 1966. In 1987, Laksov extended this result to a broader context by defining a K-Nullstellensatz for arbitrary fields. Later, in 1990, Laksov and Westin proposed strengthening to Laksov's Nullstellensatz in the form of four conjectures. Despite significant progress, determining the most effective formulation of the Nullstellensatz for arbitrary fields remains an open question. A key challenge is the abstract nature of the K-radical, which complicates its explicit computation. In this talk, I present a unified counterexample, recently given by Rati Ludhani (Nov 2024), that disproves three of the four conjectures by Laksov and Westin.
Speaker: Paramhans Kushwaha
Title: Connections in Commutative Algebra and Combinatorics.
Date and time: 17 January 2025, Friday
Time and Venue: 5:00 PM to 6:15 pm, 01- AC-207
Abstract: Monomial Ideals are the bridge between commutative algebra and combinatorics. The trend of combining commutative algebra with combinatorics originated in the pioneering work by Richard Stanley in 1975. In this talk, we will learn how a combinatorial object is nicely assigned to an algebraic object and vice versa. We will see how the algebraic properties can be studied in terms of the combinatorial data. The connections of algebraic topology and algebraic geometry with commutative algebra and combinatorics will be discussed if time permits.