Lecture 1
October 21, 2016
1:302:30pm
Room 507, Department of Mathematics, Columbia University

Speaker: Abhay Ashtekar (Institute for Gravitation & the Cosmos and Physics Department, The Pennsylvania State University)
Title: Asymptotically de Sitter spacetimes
Abstract: Important developments in geometric analysis have resolved some long standing open issues in general relativity, particularly the positivity of the Bondi energy. However, these results generally refer to asymptotically flat spacetimes. Over the last 23 decades, observations have revealed that the universe is accelerating in a manner consistent with the presence of a positive cosmological constant $\Lambda$. A positive $\Lambda$, however small, introduces very nontrivial complications in the analysis of global issues. In particular, the rich conceptual and mathematical structure that has been used for some 50 years to describe gravitational waves and, in particular, the Bondi energy requires a significant overhaul. I will explain these difficulties and their resolution in the weak field limit. I will conclude by sketching the generalization that is necessary to include full, nonlinear general relativity. This area represents a fertile ground for future developments at the interface of geometric analysis and general relativity.

Lecture 2
October 21, 2016
3:304:30pm
Room 507, Department of Mathematics, Columbia University

Speaker: Henri Roesch (Department of Mathematics, Duke Universty)
Title: Proof of a Null Penrose Conjecture using a new Quasilocal Mass
Abstract: We define an explicit quasilocal mass functional which is nondecreasing along all null foliations (satisfying a convexity assumption) of null cones. We use this new functional to prove the Null Penrose Conjecture under fairly generic conditions.
