On 3+1 Lorentzian Einstein Manifolds with One Rotational Isometry

Abstract

Differentiable manifolds whose Ricci curvature is proportional to the metric are called Einstein manifolds. Such manifolds have been central objects of study in differential geometry and Einstein's theory for general relativity, with some strong recent results.

In this talk, the speaker will focus on positively curved 3+1 Lorentzian Einstein manifolds with one spacelike rotational isometry. After performing the dimensional reduction to a 2+1 dimensional Einstein's equations coupled to 'shifted' wave maps, the speaker will prove two explicit positive mass theorems: i) for CMC slices in expanding region, and ii) for maximal slices in stationary region.

About the speaker

Dr. Nishanth Gudapati obtained his PhD from Freie Universität Berlin in 2014 (where he was also a member of the International Max Planck Research Schools and Berlin Mathematical School). He then spent a year at the Johns Hopkins University as a Postdoctoral Instructor. He is currently a DFG Postdoctoral Fellow at Yale University.

Dr. Gudapati’s research is mainly focused on partial differential equations and differential geometric aspects of Einstein's equations for general relativity.

About the program

For more information, please refer to the program website http://iasprogram.ust.hk/inverseproblems for details.