EVENT DETAILS AND ABSTRACT

Title: Geometric flows, G2-structures and 3-Sasakian geometry
Speaker: Jason Lotay
Speaker Info: University of Oxford
Brief Description:
Special Note:
Abstract:

Geometric flows give a useful analytic tool to study important problems in geometry and topology. A key example is the Ricci flow, which (after possibly rescaling) has Einstein metrics as its critical points. In 7 dimensions, 3-Sasakian geometry leads to two natural Einstein metrics with positive scalar curvature, both of which are induced by special structures known as nearly parallel G2-structures. The nearly parallel G2-structures are critical points (again up to scaling) for two different flows in G2 geometry: the Laplacian flow and the Laplacian coflow. In this talk, I will describe how the behaviour is very different for all these geometric flows on 3-Sasakian 7-manifolds, particularly in terms of the stability of the critical points. This is joint work with A. Kennon.