Sathya Rengaswami

Hi! I’m Sathya, a problem-solver by nature and mathematician by profession. This website is a window to my research interests, learnings and my creative outputs. Please explore, and reach out if you want to find out more about my work!

Current Research

I am currently a Postdoctoral Research Fellow at the Army Research Lab, where I am working on the applications of deep learning to manifold navigation. I build PyTorch models capable of handling timeseries arising in navigation. In addition, I design Monte Carlo algorithms on manifolds to simulate diffusions and autoregressive processes on manifolds.

Independent Projects

Besides my primary research topic, I enjoy working on data analysis competitions hosted on Kaggle. I build machine learning modelos to solve real-world problems. Please check out my GitHub for some of my solutions.

Previous Research

• Graph Ricci curvature and its applications to clustering on graphs
• Mean Curvature Flow and its applications to smoothing data
• The Kuramoto model and the phenomenon of synchrony

Apart from theoretical aspects, there is a strong emphasis on algorithms, programming, computation, data processing and visualization in my current research.

PhD Thesis Research

My PhD thesis is on the subject of geometric flows, a confluence of partial differential equations, convex geometry and Riemannian manifolds, with applications from mathematical relativity to image processing, edge detection etc. Intuitively, think of this as a process that deforms irregular, wrinkly surfaces into more nice, regular ones. It is modeled on heat diffusion, where curvature spreads from wrinkly regions into flat regions to create more uniform shapes.

I explore “ancient solutions” to fully nonlinear curvature flows, the well-studied mean curvature flow being a particular case thereof. This work adds to our understanding of the general phenomenon of geometric flows, by studying it from a point of view of very general families of flow speeds and exploring how the choice of flow speed affects the shapes of solutions. I was mentored by Drs. Theodora Bourni and Mathew Langford.

Master’s Research

During my Master’s, I worked on the phenomenon of synchrony, which at the intersection of dynamical systems and differential equations, and has applications to mathematical biology, power systems etc. Synchrony is ubiquitous in the natural world, seen in its most splendid form in the arising of spontaneous synchrony in fireflies. The Kuramoto Model is a powerful mathematical model that captures this phenomenon, and this is the subject of my Master’s research.

Outside Professional Life

When I’m not programming or doing math, I’m playing tennis, dancing Salsa, or going for a walk in nature.