Kunyi Ma's Webpage

About Me

Picture of mine

Hi, this is Kunyi (Mark) Ma 马坤一, a Mathematician in PDE Analysis.
I'm currently a first year Columbia University Mathematics PhD . I graduated from New York University Shanghai in Fall 2023 with a Bachelor of Science in Honors Mathematics and Data Science (Mathematics Concentration). My Senior Thesis mentors are Prof. Vahagn Nersesyan in Mathematics and Dr. Zhuang Su in Data Science.
Here is my personal CV. Here is my list of Mathematics Courses in Undergraduate Studies.

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 .

Reading Seminar: Informal Reading Group on Hyperbolic PDEs and General Relativity

This is an informal reading seminar hosted by Prof. Elena Giorgi, cohosted by Ethan Hall and Jingbo Wan. We do weekly presentations using the notes on nonlinear wave equations by Jonathan Luk, as well as recent papers and crash course in GR.
Here is my Notes for Luk's notes.
Here is the link to our website Informal Reading Seminar on General Relativity .

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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Collection of my Mathematics Notes

Working on that...

My Life and Hobbies

Love Life

My girlfriend is Lillian Zhang, second year NYU Math PhD student. We've gone through a lot in our days at New York, from Century Park to Flushing, from Newport to Coney Island. We buried ourselves in the love tales at Seattle as well as in the forest and valleys at YellowStone. Our anniversary is October 7th. It is our 2nd Anniversary ! 2006

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.