My research focuses on geometric evolution equations.  These are partial differential equations which model various natural physical and geometric processes and their analysis requires using a rich variety of techniques from various fields.  They are very powerful tools for answering questions in topology and geometry, most notably exemplified in Perelman's resolution of the Poincare and Geometrization Conjectures. Real world applications are found in fields as diverse as statistics, image processing, and general relativity.  I welcome all inquiries from motivated students.