As a mathematician, I am currently interested in developing fast algorithms for high-dimensional data analysis, particularly for various notions of geometric or topological “structure” in data, using ideas and methods from dynamics, global analysis, algebraic topology, and probability. I find it fascinating when any of these fields sheds light on the others, and especially rewarding when such viewpoints enable new algorithms in the discrete setting with stronger or faster guarantees.
I also like to study questions in global analysis, topology, and dynamics that are stimulated by biological questions, especially for networks, cell complexes, and collective motion. These questions may have a stochastic component as well.
Areas of Interest
- (Computational) Topology and (Computational) Geometry
- Cell Complexes
- Multiscale Analysis
- Mathematical Biology
- Algorithms for High-Dimensional Data Analysis
- Randomized Algorithms
- (Stochastic or Topological) Dynamical Systems (on complexes and networks)