Student Talks 2025

Table of Contents

All expository talks given by students of ISI Bangalore in the year 2025 at our Math Club are listed below.

Spring 2024

EP2506: An Introduction to Causal Inference #

Speaker: Samadrita Bhattacharya (B.Math, 2nd year)
Abstract: The study of causation becomes essential in statistics when we want to understand the story behind the data, to a degree of depth greater than just correlation. It also explains anomalies in datasets that otherwise make no sense. It has far reaching applications in fields ranging from machine learning to medical research and business analytics. This talk will serve as a small introduction into this vast avenue of research, discussing the fundamental concepts required to venture into it. I will talk about Causal Graphs, a simple diagramatic representation of causal information using directed graphs, and use simple causal graphs to understand complex scenarios.
Notes: [TBU]
Video: [TBU]
Date and Time: Saturday, 22nd March 2025, 11:00 AM - 1:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Tejas Varma (B.Math, 3rd year)
Abstract: Hasse’s Local-Global Principle is a technique used to determine if Diophantine equations have solutions (in the integers or rational numbers) by studying them over the real numbers and the p-adic fields. This method has proved itself to be particularly helpful in the study of quadratic forms. We will introduce the p-adic fields and demonstrate a few results, such as the Hasse-Minkowski theorem, that make use of the principle. We will also discuss a few applications and tackle some classical problems in Number Theory including Legendre’s Three Squares Theorem and Lagrange’s Four Squares Theorem. Time permitting, we will spend some time on integral quadratic forms in particular and try to understand the extent to which this principle may be applied.
Notes: [TBU]
Video: [TBU]
Date and Time: Sunday, 9th February 2025, 11:00 AM - 1:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Daibik Barik (B.Math, 2nd year)
Abstract: Fuzzy Set Theory, developed by Lotfi A. Zadeh in 1965, generalizes classical set theory by incorporating graded membership, where elements are members of a set with degrees in the unit interval [0,1] instead of binary membership. This generalization offers a formalism for dealing with vagueness and uncertainty.
In this lecture, we define fuzzy sets and their basic operations, such as union, intersection, and complement, with corresponding algebraic properties. We discuss fuzzy relations, their composition, and important properties. The discussion is extended to fuzzy logic, where we discuss fuzzy implication, and their use in decision-making.
We also briefly discuss fuzzy graphs and fuzzy topology, emphasizing their use in combinatorial optimization and topological structures. Throughout the lecture, we introduce important theorems, along with example illustrations emphasizing their importance. The session ends with open research problems, especially in the intersection of fuzzy structures with graph theory and topology, challenging further research in this rich mathematical discipline.
Notes: [TBU]
Video: Available here
Date and Time: Saturday, 8th February 2025, 11:00 AM - 1:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Avyaktha Achar (B.Math, 2nd year)
Abstract: Axiomatic set theory is a branch of mathematics that serves as a formal foundational system for the whole of mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice.
In this talk we will motivate the necessity for an axiomatic approach to set theory as opposed to “Naive” set theory, which was done historically but turned out to be plagued with paradoxes.
Then we will move on to the popular axiomatic approach called Zermelo–Fraenkel set theory, and discuss the main axioms of this system with motivation, and study many important notions, including algebra of sets, functions, relations etc.
We will briefly go over the set theoretic construction of natural numbers, integers, rationals, reals and complex numbers, which demonstrate how mathematics can be “embedded” into set theory.
Amongst the axioms, we will particularly spend some time on the deeper axioms such as the Axiom of Choice (and some of its equivalent versions like Zorn’s Lemma and Well-Ordering principle), as well as on the Axiom of Replacement, which will allow us to construct Cardinal numbers and Ordinal numbers formally, and do arithmetic on them.
Notes: [TBU]
Video: Available here
Date and Time: Saturday, 1st February 2025, 11:00 AM - 1:00 PM
Venue: G-26 Classroom, Academic Building

Speaker: Bhavesh Pandya (B.Math, 3rd year)
Abstract: The Riemann Mapping theorem is a beautiful result in complex analysis stating that any simply connected domain (G\in \mathbb{C}) is conformally equivalent to open unit disc (\mathbb{D}) if and only if G(\not=\mathbb{C}). We will define conformal equivalence and fractional linear transformations to give some examples of biholomorphic maps between two domains in (\mathbb{C}). Then we will prove the Riemann Mapping Theorem while proving some intermediate results.
Notes: [TBU]
Video: Available here
Date and Time: Sunday, 19th January 2025, 11:00 AM - 1:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Devansh Dhar Dwivedi (B.Math, 2nd year)
Abstract: The graph reconstruction conjecture is a famous problem in the area graph theory, posed by Paul Kelly and Stanislaw Ulam in 1941. It asks whether a graph can be uniquely determined from all of its vertex-deleted subgraphs.This talk would revolve around exploring the families of graphs for which this problem is known to have an affirmative answer.We would talk about the properties of a graph that could produce a given set of vertex deleted subgraphs.The motive of this talk would be to get a well rounded perspective on this problem as well as various problems related to it.
Notes: [TBU]
Video: [TBU]
Date and Time: Saturday, 11th January 2025, 11:00 AM - 12:30 PM
Venue: 2nd Floor Auditorium, Academic Building