“Half wandering, half wondering”

Welcome to my research webpage. You'll find a detailed description below.
Mathematical research is a challenging domain for most, and I am no different :)
Key Interests: Graph Theory, Spectral Methods, Combinatorics
General Interests: Algorithms, Linear Algebra, Computational Biology

Conference Publications

On Asymmetric Colorings of Graphs (2025)

Conference: Joint Mathematics Meetings 2025 | By AMS at Seattle, United States

Mentor: Prof. Puck Rombach (Department of Mathematics, University of Vermont)

As part of my Polymath Jr. (REU) project group, I presented our work on asymmetric graph colorings. This project established a reduction framework for computing asymmetric colouring numbers of disjoint graph unions, combining inclusion & exclusion principles with prime-factor analysis. The results contribute new bounds and techniques for understanding structural rigidity in graphs under colouring constraints. A preliminary (redacted) copy of the work can be found here.

Discrepancy Minimisation: Algorithms & Bounds (2025)

Conference: STCS Annual Symposium 2025 | By TIFR at Mumbai, India

Guide: Prof. Akash Kumar (Department of Computer Science, IIT Bombay)

At the Annual Symposium of the School of Technology and Computer Science, I spoke on my guided research into combinatorial discrepancy. The work examined symmetry in set systems via linear-algebraic formulations, scrutinising the Beck-Fiala theorem, the Partial Colouring Lemma, and related algorithms. The project developed sharper bounds on discrepancy, contributing to the broader effort of quantifying uniformity in combinatorial structures. The talk has been recorded as well and can be found here.

Research Experience

Over the course of my undergraduate career (2023 onwards to be precise) I have indulged myself in a number of learning ventures aside from college coursework. Initially they were expository in nature, and my intention was to gain informative exposure. Soon after I took up research-themed projects where I was expected to internalise some concept(s) and use the acquired knowledge to make non-trivial progress in the respective domains.

Given my experience (or the lack thereof) this usually looked like picking some special case and working it out extensively, or trying to obtain explicit results for certain structures. The research experiences which led to successful outcomes thus far have been detailed above. The rest are described below. Note that this webpage is a meant to be an expository (and occasionally light-hearted) treatment of my work. A formal account is present in my CV, to obtain which the reader is requested to contact me.

Graph Algorithms for Satellite Beam-Pattern Design

Research Internship: Aalborg University, Denmark (2025)

Guides: Prof. Petar Popovski, Prof. Israel Leyva-Mayorga [Electronic Systems, Aalborg University]

I explored novel beam-hopping strategies aimed at optimising throughput in satellite communication systems. By leveraging Laplacian-normalised spectral clustering and graph-colouring methods, I developed techniques to minimise interference across beams. This work demonstrated a tangible impact, achieving up to 15% performance improvements on low-earth-orbit models compared with conventional benchmarks.

Spectral Graph Sparsification on Weighted Graphs

R&D Project: Computer Science, IIT Bombay (2025)

Guide: Prof. Akash Kumar [Computer Science, IIT Bombay]

Here I am investigating spectral sparsification through the lens of discrepancy theory. The project focuses on balancing net resistance retention with efficient partitioning, seeking principled algorithms that preserve key spectral properties while reducing graph complexity. This line of inquiry aims to contribute both theoretical insights and practical tools for large-scale graph analysis.

Modelling Bacteria Spread in Populations

NSF REU: Polymath Jr. (2025)

Guide: Prof. Brittany Stephenson, Prof. Cara Sulyok [Mathematics, Lewis College]

In this mathematical biology group project, I constructed differential equation models to study the spread of Clostridium difficile within populations. The research combined sensitivity analyses and parameter optimisation to ensure robustness and generalisability, while drawing on existing literature to anchor the models in biological reality. The outcome was a framework that not only captured population dynamics but also highlighted potential applications for public health modelling.

Expository Work

  • Multiplicative Number Theory (2024)
    Under Prof. Kummari Mallesham (Mathematics, IIT Bombay)
    As part of an expository exploration of analytic number theory, I studied and presented Dirichlet’s theorem on primes in arithmetic progressions, drawing from Davenport’s Analytic Number Theory. The work not only traced the proof in detail but also highlighted its far-reaching implications in understanding the distribution of prime numbers.
  • Formal Dissemination of Mathematics (2023)
    Under Prof. Rekha Santhanam (Mathematics, IIT Bombay)
    I engaged in outreach by delivering talks to schoolchildren, dramatising mathematical ideas through storytelling. This effort aimed to make abstract concepts more approachable, with a particular focus on explaining key statistical ideas in ways that connected with younger audiences.
  • Arithmetical Functions & Möbius Theorem (2022)
    Under Prof. Sudhir Ghorpade (Mathematics, IIT Bombay)
    In a seminar setting, I discussed classical number theoretic tools such as Möbius functions and the Möbius Inversion Theorem. The presentation emphasised their elementary applications, providing insight into how these functions form a bridge between algebraic properties and analytic techniques.