Informal Reading Seminar on General Relativity
We meet on Fridays from 2:30pm to 4pm in room 528 to go over lecture notes in Hyperbolic PDEs and General Relativity and present recent interesting preprints.
- January 31, 2025: Sven will present his work on pp-waves
- February 7, 2025: Dawei will start a few lectures presenting the nonlinear stability of Minkowski space
- February 14, 2025: Dawei will continue to talk about the nonlinear stability of Minkowski space
- February 21, 2025: Dawei will continue to talk about the nonlinear stability of Minkowski space
- February 28, 2025: Jingbo will start talking about his thesis on the nonlinear stability of Reissner-Nordstrom black hole.
- September 16, 2024: Mark will present the first two sections of Jonathan Luk's lecture notes
- September 23, 2024: Ethan will present the third section of Jonathan Luk's lecture notes and Jingbo will talk about "Regularity of the Future Event Horizon in Perturbations of Kerr".
In this talk, I will begin by reviewing some basic concepts in GR, with a particular focus on the frames used in Giorgi-Klainerman-Szeftel-Shen’s Kerr stability result, as well as the geometry of null hypersurfaces. After covering these preliminaries, I will provide an overview of the goals and key strategies of the paper "Regularity of the Future Event Horizon in Perturbations of Kerr". This talk is designed to help those interested in the paper to easily follow and explore it further on their own.
- September 30, 2024: Ethan will continue presenting the third section of Jonathan Luk's lecture notes and Jingbo will continue talking about "Regularity of the Future Event Horizon in Perturbations of Kerr".
- October 7, 2024: Mark will present the fifth section of Jonathan Luk's lecture notes and Jingbo will continue talking about "Regularity of the Future Event Horizon in Perturbations of Kerr".
- October 14, 2024: Ethan will present the sixth section of Jonathan Luk's lecture notes
- October 21, 2024: Dawei will talk about formation of trapped surfaces.
- October 28, 2024: Dawei will continue talking about formation of trapped surfaces.
- November 11, 2024: Dawei will finish talking about formation of trapped surfaces.
- November 18, 2024: Mark will continue covering Jonathan Luk's lectures.
- November 25, 2024: Jingbo will talk about
Gluing Construction of Initial Data Sets
In this talk, we explore the gluing construction of initial data sets, focusing on the asymptotically flat regime. We begin by introducing the basic notions, including the gluing problem for initial data sets and the role of conserved physical quantities as obstructions to the linearized problem. Since the gluing construction reduces to inverting specific divergence operators while preserving prescribed support properties, we will discuss the Bogovskii-type operators and conic operators introduced in the work by Mao, Oh, and Tao. These tools provide a systematic approach to addressing the gluing problem in this context. Reference: Mao, Y., Oh, S.J., & Tao, Z. (2023). Initial data gluing in the asymptotically flat regime via solution operators with prescribed support properties. arXiv preprint arXiv:2308.13031 (https://arxiv.org/abs/2308.13031).
- December 2, 2024: Jingbo will continue talking about gluing construction of initial data sets.
- December 11, 2024: Jingbo will finish talking about gluing construction of initial data sets.
The organizer,
Elena Giorgi