BIMSA > BIMSA General Relativity Seminar Flexibility of initial data in general relativity
Flexibility of initial data in general relativity
Organizers
Lars Andersson , Alejandro Torres-Orjuela , Xiaoran Zhang
Speaker
Zhongkai Tao
Time
Friday, January 23, 2026 4:30 PM - 5:30 PM
Venue
A3-2-301
Online
Zoom 787 662 9899 (BIMSA)
Abstract
The initial data of the vacuum Einstein equations on a spacelike hypersurface satisfy the Einstein constraint equations. It is an underdetermined PDE system. We exploit the underdeterminedness to find nontrivial solutions of the Einstein constraint equations with interesting properties. A key ingredient is the construction of Bogovskii-type operators for underdetermined PDEs satisfying a robust symbol condition. The Bogovskii-type operators have favorable support and regularizing properties, allowing us to manipulate the solutions flexibly. This is based on joint work (partly in progress) with Philip Isett (Caltech), Yuchen Mao (UC Berkeley), and Sung-Jin Oh (UC Berkeley).
Speaker Intro
Zhongkai Tao is currently a junior professor in mathematics at IHES. He got his PhD from UC Berkeley under the supervision of Maciej Zworski in 2025 and completed his undergraduate studies at Xi'an Jiaotong University. He is interested in spectral theory, microlocal analysis, and PDEs.