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.

Fall 2025

EP2510: Cyclotomy: The Story of How Gauss Narrowly Missed Becoming a Philologist #

Speaker: Arkapriyo Hore (B.Math, 3rd year)
Abstract: Ancient Greek geometers knew that an equilateral triangle, a square, a regular pentagon, and a regular hexagon could be constructed using only a ruler and compass, but in 1796, Carl Friedrich Gauss showed that a regular 17-gon could be constructed with just a compass and straightedge.
Behind this elegant geometry lies the story of unexpected connections — between algebra and number theory,and, also surprisingly connecting mathematics and philology. In this talk, we’ll explore how the foundations of modern algebra were laid by Gauss’s pursuit of cyclotomic equations.
There are no prerequisites for the talk other than your enthusiasm to learn mathematics, and unfold a story spanning Greece through Aachen!
Notes: [TBU]
Video: [TBU]
Date and Time: Sunday, 10th August 2025, 11:30 AM - 1:00 PM
Venue: 2nd Floor Auditorium, Academic Building

EP2509: Sampling Techniques: Learning from a Small Part of the Population #

Speaker: Pranav Agarwal (B.Math, 3rd year)
Abstract: In this talk, I will give an introduction to some basic sampling techniques that are widely used in statistics and surveys. We will start with Simple Random Sampling (SRS) and understand how it works and why it is important. Then we will look at sampling for proportions and percentages, and how we can make good estimates about a population from a small sample. Finally, we will discuss Stratified Sampling and see how dividing the population into groups can improve the accuracy of our results. The talk will include clear examples and simple explanations, but a basic knowledge of expectation, variance, and estimators is required to follow the concepts.
Notes: [TBU]
Video: [TBU]
Date and Time: Saturday, 9th August 2025, 11:00 AM - 1:00 PM
Venue: 2nd Floor Auditorium, Academic Building

EP2508: An Introduction to Complex Analysis: The Fundamental Theorem of Algebra #

Speaker: Advait Sunder (B.Math, 3rd year)
Abstract: The Fundamental Theorem of Algebra states that every non-constant complex polynomial has at least one complex root. Though algebraic in name, many elegant proofs rely on tools from analysis. In this talk, we present a complete and self-contained proof using methods from complex analysis—specifically Liouville’s Theorem—requiring only the most minimal background. All necessary results, including key ideas from complex function theory, will be developed from scratch during the talk. The presentation is designed to be accessible to first-year undergraduates with no prior exposure to complex analysis or advanced topology.
Notes: [TBU]
Video: [TBU]
Date and Time: Sunday, 3rd August 2025, 11:00 AM - 1:00 PM
Venue: 2nd Floor Auditorium, Academic Building

EP2507: Markov chains: The Common Structure Among Seemingly Different Processes #

Speaker: Rahul Kumar (B.Math, 2nd year)
Abstract: In this talk, I’ll introduce you to probability through the beautiful lens of Markov chains - no prior knowledge needed! I’ll start with basic probability concepts, then define what makes a process a Markov chain (that special “memoryless” property) and prove some fundamental results together. We’ll explore concrete examples like random walks (including the classic gambler’s ruin problem) and branching processes (as seen in nuclear chain reactions), developing powerful tools like generating functions along the way. I’ll explain why we bother classifying these as Markov chains and what makes them so useful. Finally, I’ll leave you with some deep questions to ponder, like whether a stationary distribution always exists. First-year students especially welcome - I promise to keep this accessible and engaging!
Notes: [TBU]
Video: [TBU]
Date and Time: Saturday, 2nd August 2025, 3:00 PM - 5:00 PM
Venue: G-26 Classroom, Academic Building

Spring 2025

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: Available here
Date and Time: Saturday, 22nd March 2025, 11:00 AM - 1:00 PM
Venue: 2nd Floor Auditorium, Academic Building

EP2505: Quadratic Forms and the Local-Global Principle #

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: Available here
Date and Time: Sunday, 9th February 2025, 11:00 AM - 1:00 PM
Venue: 2nd Floor Auditorium, Academic Building

EP2504: Mathematics Beyond Precision: Navigating the World of (Fuzzy) Uncertainty #

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

EP2503: Introduction to Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC) #

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

EP2502: Riemann Mapping Theorem #

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

EP2501: The Graph Reconstruction Problem #

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: Available here
Date and Time: Saturday, 11th January 2025, 11:00 AM - 12:30 PM
Venue: 2nd Floor Auditorium, Academic Building