Mass of asymptotically Euclidean manifolds using spinors and 1-forms

Abstract: The total mass of an asymptotically Euclidean manifold is an invariant from mathematical General Relativity which has fascinated geometers for many decades. In these lectures, we will discus the celebrated Positive Mass Theorem, first describing in some detail the proof by Witten which uses spinors. I will not assume any prior knowledge of spinors. We will then focus on a contemporary approach using 1-forms which arise as the differential of solutions to a certain "spacetime harmonic" equation motivated by recent work by Daniel Stern. This second part contains work by myself, Hugh Bray, Sven Hirsch, Marcus Khuri, and Yiyue Zhang.

differential geometry

Audience: researchers in the topic

( video )

---

The 2nd Geometric Analysis Festival

Series comments: Please, submit your questions to speakers at forms.gle/F8z5LjfNNwt3DD4i8

The recorded lecture videos are available at www.youtube.com/channel/UC2gHzqcv7CT1G3fa4a7sx-Q/playlists

Video Abstracts: youtu.be/uMBqmW4r8GE

For more details, please visit the webpage (will be updated later) at cosmogeometer.wordpress.com/geometric-analysis

---