New York General Relativity Seminar, 2016



Sergiu Klainerman, Mu-Tao Wang (Columbia), Dan Lee, Christina Sormani (CUNY), Michael Anderson, Marcus Khuri (Stony Brook)

Date/ Place Title and Speaker

Lecture 1

October 21, 2016


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 space-times

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 space-times. Over the last 2-3 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 non-trivial 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, non-linear 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


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 Quasi-local Mass

Abstract: We define an explicit quasi-local 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.