MS in Applied and Computational Mathematics
University of Minnesota Duluth
Sep 2018 – May 2020
BS in Statistics
Sep 2014-Jun 2018
Overall GPA: 3.76/4.0 |Manuscript Major GPA: 4.0/4.0 Ranking: 1/109
Graduate teaching Assistant
University of Minnesota Duluth
Aug 2018 – May 2020
● Conducted lectures for various UMD courses including Calculus I and Calculus III, mathematics lab.
● Assisted students with basic math, college algebra and precalculus problems.
Colloquium speaker on random matrix theory
University of Minnesota Duluth
Dec 05, 2019
● Discussed spectral empirical distributions for products of rectangular matrices
Graduate seminar speaker about Gaussian free field
Jun 17, 2019 – Jun 28, 2019
● Conducted lectures and designed materials for discrete and continuous Gaussian free field
Graduate seminar participant about Anderson model
● Focused on discrete parabolic Anderson model, Feynman-Kac formula and asymptotics for the total mass.
Computational and applied mathematics summer school
● Learned about:
A mathematical introduction to machine learning;
An introduction of computational mathematics: from models to codes;
A Fast Algorithm for Algebraic Equations and Optimization Problems.
Random matrix theory
Statistical machine learning
SLE(Schramm-Loewner Evolution) and Gaussian free field
Fractional Brownian motion
Stochastic partial differential equations and stochastic analysis
Spectral empirical distributions for products of rectangular Matrices
Jun – Sep 2019 Advisor: Yongcheng Qi
● Found transformation for eigenvalues for products of rectangular matrices, classified limiting distributions for empirical distributions, proved limiting theorem, and offered new examples.
Exponential stability for KDV equation
Mar 2019 Advisor: Zhuangyi Liu
● Proved exponential stability for KDV equation using C0-semigroup, ODE solving, and complex analysis technique.
Presenting Reasoning Programming Chinese Mathematics intuition
MatLab Mathematica LaTex R C Python SPSS
The Zhao Yue scholarship(top 1%)
Mathematics School, Jilin University
Meritorious Winner(top 8%)
Mathematical Contest in Modeling, COMAP(the Consortium for Mathematics and Its Application)
● Developed a microscopic collision model of space crafts
Self study & Freestyle exercise
■ Further study in Real Analysis Aug-Sep 2016
Real and complex analysis (Walter Rudin).
I have gone through more than half of the book which contains all chapters and all details about Real Analysis. I believe that I have a perfect understanding on this subject.
There is a proof of Euler reflection by using Cauchy’s integral theorem.
■ Further study in Functional Analysis Feb-Dec 2017
Functional analysis (Walter Rudin);
A Hilbert Space Problem Book (Paul R. Halmos).
I nearly finished the Rudin’s book only except the Part2 distributions and fourier transforms. I believe that I have a great understanding on this subject. After finishing this book, I am eager to learn more about unbounded operators and to apply functional analysis technique to other subject. What’s more, more examples on Hilbert space made me have a better understanding on Functional Analysis.
■ A study of Probability in Functional Analysis view Feb-Jun 2018
Functional Analysis for Probability and Stochastic Processes (Adam Bobrowski).
I only finished going through the first 5 chapters. The purposes for reading this book is to understand how hard it is to construct the Brownian motion and to find the deep relationship between functional analysis and probability.
■ Self-study on Stochastic differential equations Jun-Aug 2018
Stochastic Differential Equations(Springer);
Markov Chains (J. R. Norris 1998).
I only skimmed some part of these books.
■ Proof of Reynolds transport theorem Aug 2018
Reynolds transport theorem.
I was interested in this theorem since we could use it to derive the Navier-Stokes equation.
■ Further study in PDE Aug-Dec 2018
Methods of Mathematical Physics [Vol 1] & [Vol 2] (1989 R. Courant, D. Hilbert).
I was focused on Sturm-Liouville eigenvalue problem, orthogonal polynomials, asymptotic properties of Laplace operator and understanding of characteristic of PDE of first order in a geometric view.
I found an example of using hermite function to solve irregular Strum-Liouville problem.
Sturm-Liouville Theory and its Applications(M. A. Al-Gwaiz);
An Introduction to Partial Differential Equations(Michael Renardy, Robert C. Rogers).
I was focused on the proof of Sturm-Liouville theorem.
Partial Differential Equations (Jurgen Jost);
Harmonic Function Theory(Sheldon Axler Paul Bourdon Wade Ramey).
I was focused on the basic properties of harmonic functions, the generalization of maximum principle and Kelvin Transform.
■ Classical Perron-Frobenius theory and its generalization Sep 2018
Nonlinear Perron-Frobenius theory.
Krein-Rutman Theorem on the Spectrum of Compact Positive Operators on Ordered Banach Spaces;
I was focus on the proof, generalization and its application on markov chain.
■ Self-Study on Differential Geometry Sep-Dec 2018
Calculus on Manifold (Michael Spivak).
I finished the whole book, but to be honest, I did not have a perfect understanding on differential geometry.
I wrote some note about Calculation on curvilinear coordinates, Christoffel symbols, gradient, divergence and laplacian.
I also recalled an example of Surface integral in spherical coordinates during my TA in cal III.
■ Proof of Brouwer’s fixed point and invariance of domain theorem Aug 2018
■ A further study on C0-semigroup Mar 2019
Advisor: Zhuangyi Liu
Optimal polynomial decay of functions and operator semigroups;
Fine scales of decay of operator semigroups;
Conditions on the Generator of a Uniformly Bounded C0-semigroup;
Stability of C0-semigroups and geometry of Banach spaces;
On continuous dependence of roots of polynomials on coefficients (Alen Alexanderian);
Boundary Controllability of Korteweg-de Vries-Benjamin Bona Mahony Equation on a Finite Domain.
I finished my first project in which I offered a proof of the exponential stability for KDV equation.
■ Self-study on Random Matrix Apr-Jun 2019
Main Reference with online course:
Introduction to Random Matrices Theory and Practice(Giacomo Livan, Marcel Novaes, Pierpaolo Vivo)
Will a Large Complex System be Stable?
Level-Spacing Distributions and the Airy Kernel(Craig A. Tracy, Harold Widom);
The eigenvalue spectrum of a large symmetric random matrix.
I reorganize a proof of Joint Law of Eigenvalues and Eigenvector for Symmetry Random Matrix.
Introduction to random matrix theory(Todd Kemp);
Lie groups, Lie algebras, and representations -an elementary introduction (2015 Hall, Brian C);
Concentration of Measure and the Compact Classical Matrix Groups.
■ Summer research on Random Matrix May-Sep 2019
Advisor: Yongcheng Qi, Tiefeng Jiang
Spectral Radii of Products of Random Rectangular Matrices (2019 Yongcheng Qi, Mengzi Xie);
Empirical Distributions of Eigenvalues of Product Ensembles(2019 Tiefeng Jiang, Yongcheng Qi);
Spectral Radii of Large Non-Hermitian Random Matrices(2017 Tiefeng Jiang, Yongcheng Qi);
Limiting empirical distribution for eigenvalues of products of random rectangular matrices (Xingyuan Zeng).
Using the technique in previous paper, I finish a paper which resolve the limiting spectral empirical distribution for rectangular Ginibre ensemble in a general way.
■ Lecture and my own handouts about Gaussian Free Field Jun-Jul 2019
Advisor: Tiefeng Jiang
Topics on the two-dimensional Gaussian Free Field;
Conformally Invariant Processes in the Plane;
Introduction to the Gaussian Free Field and Liouville Quantum Gravity Chap 1 Definition and properties of the GFF;
Discrete Gassian Free Field & scaling limits;
Gaussian free fields for mathematicians(Scott Sheffield);
Thanks to Prof. Tiefeng Jiang, I have an experience to offer a lecture to talk about Gaussian free field. After that, I integrated some handouts and my own thinking, thus I wrote my own handout for my lecture.
■ A survey on positive definite preserving transformations on symmetric matrix space Oct 2019
Positive definite preserving linear transformations on symmetric matrix spaces;
Positive maps, absolutely monotonic functions and the regularization of positive definite matrices;
Topics in Matrix Analysis, Chap 6;
I did a survey on the classification theorems on linear and non-linear transformations which preserves positive definiteness.
■ Basic on Wiener Space, Fractional Brownian motion, Fractional Laplacian, and Fractional Gaussian fields Jan 2019-
Advisor: Tiefeng Jiang
Analysis on Wiener Space and Applications;
An Introduction to Analysis on Wiener Space. Chap 1 and Chap 2;
On measurable norms and abstract Wiener spaces;
A Modern Theory of Random Variation. With Applications in Stochastic Calculus, Financial Mathematics, and Feynman Integration;
The Malliavin Calculus and Related Topics. Chap 1 Analysis on the Wiener space and Chap 5 Fractional Brownian motion;
Ten Equivalent Definitions of the Fractional Laplace Operator(Mateusz Kwasnicki);;
Discretizations of the Spectral Fractional Laplacian on General Domains with Dirichlet, Neumann, and Robin Boundary Conditions(Nicole Cusimano, Felix Del Teso, Luca Gerardo-Giorda, and Gianni Pagnini);
Fractional Integrals and Derivatives: Theory and Applications-Gordon and Breach Science Publishers (Stefan G. Samko, Anatoly A. Kilbas, Oleg I. Marichev);
Fractional Calculus for Scientists and Engineers(Manuel Duarte Ortigueira);
Hitchhiker’s guideto the fractional Sobolev spaces(Eleonora Di Nezza, Giampiero Palatucci, Enrico Valdinoci);
Fractional Gaussian fields: a survey(Asad Lodhia, Scott Sheffield, Xin Sun, Samuel S.Watson);
Introduction to Fourier Analysis on Euclidean space(Elias M. Stein, Guido Weiss)Chap IV Symmetry Properties of the Fourier Transform;
Strong Approximation of Fractional Brownian Motion by Moving Averages of Simple Random Walks(Tama’s Szabados).