Jacob Krantz

Geometric Flows

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

Thank you for funding my research. Your generosity has enabled me to focus on my schooling this summer. I really appreciate the opportunity to learn how to do math research, and I am excited to begin my research career with a project as interesting as this one.
  • Major: Math, Computer Science
  • Sponsor: Math Team Fund
  • Mentor: Sung-Jin Oh