Geometric flows, such as the Ricci flow, Yang-Mills flow, and harmonic map flow, are natural ways to smooth out geometric objects (metric, connection, and maps, respectively). In this project, we will explore the idea of using geometric flows to develop new analytic tools for studying geometric objects. A possible goal of this project is to use geometric flows to solve problems in dispersive PDEs that involve geometric objects.
Message to Sponsor
- Major: Math, Computer Science
- Sponsor: Math Team Fund
- Mentor: Sung-Jin Oh