Check out some of my projects...
"I like crossing the imaginary boundaries people set up between different fields—it's very refreshing. There are lots of tools, and you don't know which one would work. It's about being optimistic and trying to connect things."
- Maryam Mirzakhani
My research area falls under the umbrella of algebraic combinatorics and categorical combinatorics. Previous work has included applying the theory of inverse semigroups and partial symmetries to graphs, and to generalize the Noether Isomorphism Theorems to the Category of Graphs. I am currently involved in a project generalizing the continuous notions of homotopy to graphs, using a categorical approach. It's super fun!
In a broad sense, what motivates me in this direction is the potential to develop deeper theories in combinatorics, and find the connections between combinatorics and other disciplines through category theory, rather than ad-hoc techniques.