| 13:00-13:15: | Arrival (tea/coffee) [Room 04.4.20] | ||
| 13:15-14:15: | Speaker: Jason Lotay (Oxford University) [Room 04.4.20] | ||
| Title: Lagrangian mean curvature flow and the Gibbons-Hawking ansatz | |||
| Abstract: Lagrangian mean curvature flow is a potentially powerful tool with links to symplectic topology, Riemannian and complex geometry, and theoretical physics. A key open problem in the field is the Thomas-Yau conjecture, which gives a putative criterion for long-time existence and convergence of the flow. I will discuss a recent proof of a version of the Thomas-Yau conjecture for a family of 4-dimensional manifolds, which are gravitational instantons given by the Gibbons-Hawking ansatz. This is joint work with Goncalo Oliveira. | |||
| 14:15-14:45: | Tea/coffee/cookies [Room 04.4.20] | ||
| 14:45-15:45: | Speaker: Alexander Friedrich (U Copenhagen, Denmark) [Room 04.4.20] | ||
| Title: The Hawking Energy on Small Surfaces - Expansion and Concentration Points | |||
| Abstract: The Hawking energy is a quasi local energy in General Relativity. It is used to measure the energy contained within a given volume by measuring the bending of light rays across its boundary. We work in a time slice and regard the Hawking energy as a generalized Willmore functional on spherical surfaces subject to an area constraint. The goal is to analyze the behavior of critical surfaces with small area and identify points in the ambient manifold around which they concentrate. Additionally, we obtain an expansion of the Hawking energy on small spheres. These two results allow us to identify a kind of energy density for the Hawking energy. |