- Teaching Assistant
Broadly, I am interested in applying the tools of algebraic topology to real world problems. The two subfields I am primarily interested in are topological data analysis and topological robotics. In topological data analysis, I am particularly interested in topological properties of rips complexes as well as the application of discrete morse theory in the computation of persistent homology. In topological robotics, I have worked on continuous motion planning algorithms as well as using cohomology and obstruction theory to determine the topological complexity of various spaces. Currently, I am working with configuration spaces of polygons in Euclidean space in an attempt to get stronger upper and lower bounds on their topological complexity.