Academic Projects
Graduate Projects
Reading Seminar: Functions of Bounded Variation and Minimal Surface
This is a graduate student seminar hosted jointly by Chun Szeto and Jingbo Wan, under supervision of Prof. Ovidiu Savin and Prof. Daniela De Silva. We read the book by Giusti on the subject and did weekly presentations.
Here is my Notes for the seminar.
Here is the link to our website Student PDE Seminar (Fall 2024): The Theory of Bounded Variation Functions & Regularity Analysis of the Minimal Surface PDE .
Undergraduate Projects
Onsager's Theorem and Intermittent Convex Integration for Incompressible Euler and Navier-Stokes
This is an Independent Study program with Prof. Vlad Vicol on Convex Integration Schemes in Euler and Navier-Stokes Equations in Fall 2023. I mainly studied 2 papers respectively on the flexibility part to Onsager's Theorem (the classical Convex Integration), and the Non-uniqueness of Mild Weak Solutions to NS (intermittent jets for Convex Integration).
Here is my Notes for Onsager's Theorem.
Here is my Hand-Written Notes for Intermittent Convex Integration for Navier-Stokes.
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Existence of Stationary Measure for 2D Incompressible
Navier-Stokes with Random Kick Forces and White-in-time
Noise
This is my pedagogical Senior Thesis in Honors Mathematics with Prof. Vahagn Nersesyan in Fall 2023. The goal is to show the existence of stationary measure for 2D Stochastic Navier-Stokes with
random kick forcing and with regular white-in-time noise via Bogolyubov-Krylov argument. The literature follows Chapter 1 and Chapter 2 in Mathematics of Two-Dimensional Turbulence by Kuksin-Shirikyan.
Here is my Honors Math Senior Thesis.
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On modifying Loss Function for Physics
Informed Neural Operator(PINO) to approach
Mathematics Nature in Fluid Mechanics
This is my original Senior Thesis in Data Science with Dr. Zhuang Su in Fall 2023. This project explores the mathematics possibility of Neural Operator Learning in Navier-Stokes Equations. We modified the original Data and PDE Loss
functions in PINO using regularity theory from PDE Analysis, and found a
Data Loss Norm that sees clearer turbulence flows.
Here is my Data Science Senior Thesis.
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Reading Seminar: 2nd order Elliptic Partial Differential Equations
This is an Independent Study program with Prof. Chao Li and Prof. Fanghua Lin in Summer 2023 and Fall 2023. We read through Lin-Han's book Elliptic Partial Differential Equations and Lin's newest notes Ten Lectures on Elliptic Partial Differential Equations.
Here is my sample Notes for viscosity solutions to Elliptic PDE.
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Reading Seminar: Incompressible Euler and Navier-Stokes, and Stochastic Calculus
This is Funded Dean's Undergraduate Research Program with Prof. Vahagn Nersesyan in Summer 2023. We read 2 books, The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations: An Introduction by
Vicol-Bedrossian, and Introduction to Stochastic Calculus by Evans.
Here is a sample solution to selected problems in Evans SDE by myself.
Reading Seminar: Evans Chapter 2
This is an Independent Study program with Prof. Pedro Antonio Santoro Salomão in Fall 2022. The study in Evans Chapter 2 led me to the world of PDEs.
Here is my sample Study Reflection in Evans Chapter 2.
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My Life and Hobbies
Love Life
My girlfriend is Lillian Zhang, first year NYU Math PhD student. We've went through a lot in our days at New York, from Century Park to Flushing, from Newport to Coney Island. We kissed each other in the love tales at Seattle as well as in the forest and valleys at YellowStone.
Our anniversary is October 7th.
Singing/ A Cappella
I sang Tenor 1 for Elite A Cappella (Octave Fusion) at NYU Shanghai from Spring 2021 to Fall 2022, trained by Katherine Girvin and Gabriel Song. This was among my most precious memories in undergraduate years.
Literature
I served as President of Literature Club at NYU Shanghai in year 2021-2022, and Vice President of Literature Club at Nanyang Model High School in year 2018-2019.
Movie
For example, I watched 21 movies in a week at the 12th Beijing International Film Festival.
