Research
My research interests are in differential geometry and geometric analysis. Currently I study the Ricci flow. I am interested in learning more about formulation of singularities and large-time behavior of the Ricci flow in manifolds which admit circle actions. I hope that my results can be used to understand how exactly the Ricci flow might perform the geometric decomposition of a three-manifold as time evolves. I also hope that my results may be applied to theoretical physics, namely renormalization group flows of quantum field theories. I am also interested in other geometric flows (cross-curvature flow, mean-curvature flow, etc.), and I hope to study these in the future.
Research Statement
- Research statement Here is a copy of my research statement, including a summary of my current research and my future plans.
Publications
- "Ricci flow on manifolds with circle action" (in preparation)
Ricci Flow
For more information about the Ricci flow, look at the links below.
- Ricci flow - Wikipedia
- Perelman's Ricci flow papers: 1, 2, 3
- "Notes on Perelman's papers" by Kleiner and Lott
- "Ricci flow and the Poincare conjecture" by Morgan and Tian