The Ricci flow is a geometric PDE similar to a heat equation for a Riemannian metric g. The major idea in using the Ricci flow to answer questions in geometry and topology is to evolve a starting metric on a given manifold, to some canonical, "nice" metric, from which one can draw topological conclusions about the manifold. In the various applications of Ricci flow over the years, an essential ingredient has been to know which "curvature conditions" (like nonnegative curvature operator, nonnegative isotropic curvature, nonnegative bisectional curvature etc.) are preserved for the evolving metrics under the flow. In this talk I will present a theorem of Wilking from 2011, which provides an unified framework that proves all of the previously known invariant curvature conditions.

### Graduate Student Geometry-Topology Seminar

Monday, April 24, 2017 - 3:15pm

#### Anusha Krishnan

University of Pennsylvania