My current research
Geometry and topology, the study of rigid structures on the one hand and their flexible deformations on the other, exhibit a rich interplay in low dimensions. This dynamic is worthy of consideration unto itself, but recent applications in the study of complex data sets are exciting and motivating as well. My research to date focuses on the geometry and topology of low-dimensional manifolds. Specifically, I am interested in:
- Hyperbolic 3-manifolds, Kleinian groups, and their parameter spaces
- Teichmüller spaces, moduli spaces, and their natural geometries
- Applications of geometry and topology to the study of complex data sets
Understanding the geometry and topology of 3-dimensional spaces helps us understand more deeply the nature of the space in which we live, its physical properties, and its fundamental structure.