Xiaoshuo Lin
I am Xiaoshuo Lin ( hear my first name), a first-year Ph.D. student in the Department of Mathematics at Yale University.
My research interests lie in geometric analysis and differential geometry. Or, in the language of the Map of Mathematistan, you can usually find me wandering around the northern regions, where the plains of analysis rise into the hills of differential geometry and meet the tundra of topology.
Education
- 2026 – Present: Ph.D. in Mathematics, Department of Mathematics, Yale University
- 2022 – 2026: B.Sc. in Mathematics, Hua Loo-Keng Talent Program in Mathematics, University of Science and Technology of China
- 2019 – 2022: The Affiliated High School of South China Normal University
Teaching
Resources
For non-Chinese readers, you may streamline this list to English resources only.
All works created by me are licensed under CC BY-NC-SA 4.0
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Mathematical Analysis
Real Analysis
- Honors Real Analysis Homework Assignments PDF
- Real Analysis @UCLA
Complex Analysis
- Honors Complex Analysis Homework Assignments PDF
- Errata to Complex Analysis by Elias M. Stein and Rami Shakarchi PDF
- Visualize Complex Mappings with Visualizer 1 and Visualizer 2
- Explore the Beautiful Group, \(\operatorname{SL}(2,\mathbb{Z})\)
- A Second Course in Complex Analysis @CUHK
- Modular Forms @BIMSA
Special Functions
- NIST Digital Library of Mathematical Functions
- Notes on Special Functions by Michael Taylor
- Travor Zihao Liu’s Zhihu Pages
- On Costa’s Minimal Surface Slides with Interactive Visualizations
Functional Analysis
Differential Equations
- Notes (on ODEs) and Homework Assignments PDF
- Handwritten Notes on PDEs PDF
- Linear Dynamical Systems @Stanford
- Errata to Partial Differential Equations by Lawrence C. Evans PDF
- Errata to Differential Equations, Dynamical Systems, and an Introduction to Chaos by Morris Hirsch, Robert L. Devaney, and Stephen Smale
Linear Algebra
Abstract Algebra
- Notes and Homework Assignments PDF
- Visit Group Names, Group Explorer, and Number of Small Groups for an Excursion among Groups
- Abstract Algebra @BSU Videos
- Solutions to Abstract Algebra by David S. Dummit and Richard M. Foote
Commutative Algebra
- “Commutative Algebra” by Richard E. Borcherds Videos
- Notes on Commutative Algebra @RPTU
Homological Algebra
- “Introduction to Homological Algebra” by Richard E. Borcherds Videos
- An Introduction to Homological Algebra @BIMSA
Lie Groups and Lie Algebras
- “Lie Groups” by Richard E. Borcherds Videos
- “Lie Groups and Lie Algebras” by Siqi Liu Videos
- Introduction to Lie Algebras @BIMSA
Combinatorics
- Notes and Homework Assignments PDF
- “Combinatorics” by Jie Ma Videos
- “Extremal Combinatorics” by Jonathan Noel Videos
Probability Theory
- Notes and Homework Assignments PDF with Guide on Exercises
- Advanced Topics in Probability Theory PDF
- Univariate Distribution Relationships
Stochastic Processes
- Selected Solutions to Stochastic Processes by Sheldon M. Ross PDF
- Handwritten Notes on Chapters 4–8 PDF
- Homework with Hints and Supplements @Columbia
- Applied Probability and Stochastic Modeling @UMich
- Applied Stochastic Processes @PKU
Foundations of Geometry
- Lecture Notes by Mao Sheng and Zuoqin Wang PDF
- The Foundations of Geometry by David Hilbert
General Topology
- Honors Topology Homework Assignments PDF
- Corrections to John M. Lee’s Introduction to Topological Manifolds PDF
- \(\pi\)-Base — A Community Database of Topological Counterexamples
- Dan Ma’s Topology Blog — Expository Articles in General Topology
Differential Geometry
- Honors Differential Geometry Homework Assignments PDF
- Hints and Extensions to Chapters 1–5 by Rui Xiong PDF
- Reference for Global Differential Geometry
Smooth Manifolds
- Differentiable Manifolds (MATH5003P) Homework Assignments PDF
- Corrections to John M. Lee’s Introduction to Smooth Manifolds PDF
- “Manifolds and Geometry” by Jiaqiang Mei Videos
Riemannian Geometry
- Riemannian Geometry Homework Assignments PDF
- Corrections to John M. Lee’s Introduction to Riemannian Manifolds PDF
- Ricci — Symbolic Tensor Computations for Differential Geometry
- “Analysis on Manifolds” by Alexander Grigor’yan
- Morse Theory @BIMSA
- An Introduction to Minimal Surfaces @BIMSA
Algebraic Topology
- Algebraic Topology Homework Assignments PDF
- Algebraic Topology by Allen Hatcher PDF
- Lecture Videos KIT NTU NCTS Nankai Andrews
- Honors Algebraic Topology @FDU
Characteristic Classes
- Characteristic Classes by J. W. Milnor and J. D. Stasheff PDF (Adapted from the Original LaTeX Project by the TeXromancers)
- Vector Bundles and K-Theory by Allen Hatcher PDF
- “Characteristic Classes” by Geometry Potsdam Videos
- Differential Topology @SBU
- Fiber Bundles, Characteristic Classes, and Index Theorems @BIMSA
- Cobordism, Index Theorems, and Generalized Symmetry @BIMSA
Algebraic Geometry
- The Stacks Project — An Open Source Textbook and Reference Work on Algebraic Geometry
- The Rising Sea: Foundations of Algebraic Geometry
- “Algebraic Geometry” by Richard E. Borcherds Varieties Schemes Extra Topics
- Algebraic Curves @BIMSA
- Notes on Plane Algebraic Curves @RPTU
- Notes on Algebraic Geometry @RPTU
Freshman Seminar
- Asymptotics and Numerical Approximation of the Riemann \(\zeta\) Function Slides
Scientific Programming
- Random String Plucking and Overtone Synthesis in Python PDF
General Physics
- Quick Notes Mechanics Thermotics Electromagnetism Optics Atomic Physics
- The Feynman Lectures on Physics
Useful Links
Mathematics
- arXiv
- Mathematics Stack Exchange
- MathOverflow
- Banana Space
- Wolfram Alpha
- Sage Reference Manual
- Simons Center for Geometry and Physics
- Institute of Geometry and Physics
- BIMSA Courses
- YMSC Video Archive Courses Lectures
- USTC Recorded Lecture Series
- An Infinitely Large Napkin
- The Legacy of FDUer
- The Online Encyclopedia of Integer Sequences
- Sequence Machine
LaTeX
- Overleaf — Online LaTeX Editor
- TeX Stack Exchange
- TeX to Unicode
- Create LaTeX Tables
- Detexify — Find the LaTeX Command for a Symbol You Can Draw but Not Name
Utilities
- Corpus of Contemporary American English
- Screen Mirroring Receiver Sender
- DjVu to PDF
- Shields — Concise, Consistent, and Legible Badges