Research

• Informal Reading Seminar on PDE and Harmonic Analysis (Website)

Notes on PDE and Harmonic Analysis (PDE, HA)

• These notes were started as I prepared for my preliminary exam (more info here). They serve as foundational knowledge for my research and are evolving over time. 

Global Stability of Minkowski Spacetime (Link)

• I provide an introduction to the seminal work of Christoudoulous and Klainerman on global nonlinear stability of Minkowski spacetime. In PDE language, this is a small data global wellposedness result for the Einstein vacuum equation.

• This note also serves as the final project of MATH 636 at the University of Michigan, a course on mathematical general relativity taught by professor Lydia Bieri in Winter 2024.

Introduction to Minimal Surfaces (Link)

• I provide an introduction to the theory of minimal surfaces. I am primarily following A Course on Minimal Surfaces by Colding and Minicozzi, and I also referred to this note by Ao Sun. Many details were reconstructed according to my personal preference. 

• This note also serves as the final project of MATH 635 at the University of Michigan, a course on Riemannian Geometry taught by professor Lydia Bieri in Winter 2023.

The Prime Number Theorem (Link)

• I provide an exposition on the proof of the prime number theorem. The approach I am following is adapted from professor Rowan Killip's lecture notes for MATH 246B at UCLA, while many intermediate gaps were filled by myself. 

• This note also serves as the final project for a class MATH 205A at UCLA, taught by professor William Duke on analytic number theory in Fall 2020.