Pure Maths Colloquium: Ricci flow and the heat equation
16 February 2009 16:15 in CM 107
We will first describe the differential Harnack inequality for the heat equation on a manifold. Then we will discuss Perelman's amazingly analogous Harnack estimate for the Ricci flow. It gives rise to monotone quantities, which are essential in understanding singularities occurring in the Ricci flow. We will conclude with a new monotonicity result and its application to singularity analysis.