My current research is in the dynamics of wildland fire, but I am interested in the mathematical structure of a wide variety of complex, multi-scale natural phenomena. As a member of the applied dynamics group, I approach these problems by studying their underlying geometry. In particular, given a set of differential equations that describe the state of a system as it evolves in time, I study the trajectories of the resulting dynamical system to glean information about the behavior of the physical system.
In the summer of 2021, I was an intern with the Center for Forest Disturbance Science. I worked with researchers in ecology and fire science to develop a novel method of characterizing fine scale fuel structure in Lidar data using topological data analysis. The tools I developed can be found on my Github: https://github.com/o-chandra/lidar-tda/.
My undergraduate research was in vertex operator algebras, an area at the intersection of modern physics and algebra. In particular, I studied the fermionic and bosonic vertex algebras, investigating their generators and invariants under the action of the integers modulo 2. My undergraduate thesis can be found here and a related poster here. This work also led to a paper, jointly published with Michael Penn and Hanbo Shao.