Projects & Research
I am drawn to mathematical modelling, algorithms, and urban systems: the places where a clean mathematical idea has to survive contact with budgets, sensors, and cities.
Research · Ongoing
At the University of Chicago's Guha Lab, I am investigating how water quality can be predicted using machine learning, spatial algorithms, and interpolation algorithms. For this, I am comparing 6 different models on 3 parameters in 3 rivers.
Research · Ongoing
At IIT Bombay, I am developing mathematical models using algorithms for urban delivery networks that balance operating costs with greenhouse gas emissions. The research considers a two-stage system involving trucks, electric two-wheelers, and delivery robots. I am examining how different budgets and transport choices affect the tradeoff between cost and emissions.
Details of Cost against emissions in urban delivery networks →
Team project · BMC pilot, CSR funded
FloodGuard is a team project developing an affordable system to monitor conditions inside stormwater drains and provide early alerts. I lead engineering, mathematical modelling, and data analysis, using regression to relate sensor readings to water flow and evaluate measurement error. I also contribute to device design and microcontroller programming, while exploring how accuracy, cost, and deployment constraints can be balanced. The team presented the prototype to officials of the Brihanmumbai Municipal Corporation in Mumbai, where it is being taken forward as a BMC pilot with CSR funding, and wrote up the bench results in a research paper.
Published research · Published
This research investigates where sensors should be placed in a stormwater network to improve coverage within a limited budget. Using drainage-network data from Bengaluru, I modelled the system as a graph and compared random placement, greedy selection, and exact optimisation. I examined how sensor budgets and coverage assumptions affect the results, alongside the practical limitations of translating a mathematical solution into a deployment plan.
Details of Optimising sensor placement in stormwater networks →
Independent research · Ongoing
I am investigating quadratic Diophantine equations, modular arithmetic, and Pell's equations through proof-based analysis. The question behind it is simple to state: when does an equation like x squared minus D times y squared equal 1 have whole-number solutions, and how can they all be found? It is the pure-mathematics side of my work, and it grew out of my proof-based coursework in Mathematical Thinking and Modern Algebra.
Details of Pell's equation and quadratic Diophantine equations →