Calendar

In this talk, we will discuss a quasi-local Penrose inequality with charges for time-symmetric initial data of the Einstein-Maxwell equation. Namely, we derive a lower bound for Brown-York type quasi-local mass in terms of the horizon area and the electric charge. The inequality we obtained is sharp in the sense that equality holds for surfaces in the Reissner-Nordström manifold. This talk is based on joint work with Stephen McCormick.

We give the first examples of codimension-1 knotting in the 4-sphere, i.e. there is a 3-ball B_1 with boundary the standard linear 2-sphere, which is not isotopic rel boundary to the standard linear 3-ball B_0. Actually, there is an infinite family of distinct isotopy classes of such balls. This implies that there exist inequivalent fiberings of the unknot in 4-sphere, in contrast to the situation in dimension-3. Also, that there exists diffeomorphisms of S^1 x B^3 homotopic rel boundary to the identity, but not isotopic rel boundary to the identity. Joint work with Ryan Budney.

Future schedule is found here: https://scholar.harvard.edu/gerig/seminar