Summer course: Mathematics of Gravitational Radiation

Overview

This is a two-week summer course on the mathematics of general relativity. It will be held at Astro-Math 440, NTU during July 15th~29th, 2019.

Einstein’s prediction of gravitational waves was only rigorously justified in 1960’s. The work of Bondi and Trautman and their collaborators established the mass loss formula that gave the first nonlinear theoretical verification of gravitational waves. Subsequent work of Penrose and his contemporaries defined the conformal compactification near future null infinity which paved the background for a systematic study of gravitational radiation. The development culminated in the breakthrough in 2015 when gravitational waves were detected by mankind for the first time. While most of the quantitative study in gravitational waves detection rely on numerical methods and the physical theory established earlier, the study of the Cauchy problems of the Einstein equation in the past few decades (in particular, the Christodoulou-Klainerman theory) suggested that the structure of future null infinity is more erratic and irregular than the picture portrayed in the physical theory. Recent progresses in geometry and PDE in mathematics provide powerful and timely tools to reexamine, reinforce, and update the theory. In this minicourse, we will discuss the mathematical theory of gravitational radiation which includes, but not limits to, the Bondi-Trautman mass loss formula, the BMS group, asymptotically hyperboloids, memory effect, the Cauchy formulation of Einstein’s equation, and future null infinity. This minicourse will gather researchers working on the frontier of recent development and aim to provide a sound foundation to work on related areas.

Speakers

• Po-Ning Chen 陳泊寧, University of California, Riverside
• Pei-Ken Hung 洪培根 , Massachusetts Institute of Technology
• Jordan Keller, Harvard University
• Junbin Li 黎俊彬, Sun Yat-Sen University
• Henri Roesch, Columbia University
• Mu-Tao Wang 王慕道, Columbia University
• Ye-Kai Wang 王業凱, National Cheng Kung University

Organizers

• Po-Ning Chen 陳泊寧, University of California, Riverside
• Mao-Pei Tsui 崔茂培, National Taiwan University
• Mu-Tao Wang 王慕道, Columbia University
• Ye-Kai Wang 王業凱, National Cheng Kung University