Student Talks 2026

Table of Contents

All expository talks given by students of ISI Bangalore in the year 2026 at our Math Club are listed below.

Fall 2026

EP2605: Counting Arcs on Punctured Discs
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Speaker: Pragalbh Kumar Awasthi
Abstract: In this talk, we will discuss a sharp extremal problem concerning collections of essential arcs on punctured disks. Specifically, we consider families of pairwise non-homotopic arcs with endpoints on the boundary of a punctured disk, under the condition that any two arcs intersect at most twice. We will present the proof of the optimal upper bound on the size of such a family, together with constructions showing that the bound is sharp. Along the way, we will see how local intersection patterns lead to global constraints, illustrating the rich interplay between topology and combinatorics in the study of surfaces.
Video: [TBU]
Date and Time: Sunday, 9th August 2026, 11:00 AM - 1:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Hrishik Koley (M. Math, 2027)
Abstract: How many points must we place in the plane before some \(k\) of them are forced to form a convex polygon? Starting from the elementary fact that five points in general position always contain a convex quadrilateral, we introduce the Erdős-Szekeres function \(ES(k)\) and the celebrated Happy Ending conjecture. We then explore a connection with the Erdős-Szekeres monotone subsequence theorem, more precisely it’s geometric analogue, as well as a special case of Ramsey’s theorem called the Ramsey’s theorem for triples.
Video: [TBU]
Date and Time: Tuesday, 28th July 2026, 6:00 - 7:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Spring 2026

Speaker: Shankha Suvra Dam (B. Math, 2026)
Abstract: How hard can it be to cut a cake fairly? If you’ve ever had to split a cake with various toppings, you know the struggle: everyone wants a different piece! How can you ensure the distribution is fair? And mathematically speaking, how do you even go about defining what “fair” looks like in this context?
That is exactly what we will discuss in this talk. We will start by defining the rigorous notions surrounding fairness and then review the foundational body of work in this field. All of this will culminate in the monumental 2016 result by H. Aziz and S. Mackenzie, which finally provided an upper bound (admittedly, a completely ridiculous one) for the number of steps required to guarantee a fair division of a cake among \(n\) agents.
Notes: [TBU]
Video: Available here
Date and Time: Saturday, 14th March 2026, 4:30 - 6:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Aritrabha Majumdar (B. Math, 2026)
Abstract: The fractal percolation process was first described in the 1970’s. However, to the largest extent, it was not until the advent of that this system first came to the attention of the mathematicians; in particular, those of us with an interest in percolation problems. The amusing feature of both the ordinary percolation problems and this multi-scale analogue is that while the entire set-up can be described in a few sentences, the systems provide a seemingly inexhaustible supply of interesting phenomena and challenging problems.
Here we would first define the model, analyse some of its properties as a Galton - Watson Branching Process, and we would conclude the talk by discussing some more generalization and some related models.
Video: Available here
Date and Time: Monday, 26th January 2026, 3:00 - 5:00 PM
Venue: 2nd Floor Auditorium, Academic Building

Speaker: Ramdas Singh (B. Math, 2027)
Abstract: Classical differentiation is often too rigid: functions that behave well under integration may fail to have pointwise derivatives. This talk introduces weak differentiation, motivated by integration by parts and the Lebesgue integral. We define weak derivatives, examine basic examples, and show how classical results extend in this setting, leading naturally to the Sobolev space \(H^1\). The Poincaré inequality is also discussed as a first illustration of why such spaces are central in analysis and variational problems. A working knowledge of Lebesgue integration and normed and inner product spaces may be required.
Video: Available here
Date and Time: Sunday, 18th January 2026, 11:00 - 1:00 PM
Venue: G-26 Classroom, Academic Building

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