June 4, 2011 (Sat) 10:05--11:05, 14:00--15:00 Lecture Hall (Room No. 420) Research Institute for Mathematical Sciences Kyoto University, Kyoto, Japan |

Simon Brendle

(Stanford University)

(Stanford University)

**Abstract**

A fundamental question in Riemannian geometry is to find
canonical metrics on a given smooth manifold. In the 1980s, R. Hamilton
proposed an approach to this question based on parabolic partial
differential equations. The goal is to start from a given initial metric
and deform it to a canonical metric by means of an evolution equation.
There are various natural evolution equations for Riemannian metrics,
including the Ricci flow and the conformal Yamabe flow. We will discuss
the global behavior of the solutions to these equations. In particular, we
will describe how these techniques can be used to prove the Differentiable
Sphere Theorem.

References: |
S. Brendle, Evolution equations in Riemannian geometry, Japanese Journal of Mathematics, Volume 6-1, (2011), pages 45--61. [Article (Springer Link)] |