Chunyin Siu (Alex) is a postdoctoral scholar in the Brain Dynamics Lab, led by Prof. Mannish Saggar, at the Stanford University School of Medicine. He specializes in topological data analysis and its application in analyzing neuroimaging data.

He got his PhD degree in Applied Mathematics at Cornell University under the supervision of Prof. Gennady Samorodnitsky. Before that, he got this MPhil. degree in Mathematics at the Chinese University of Hong Kong under the supervision of Prof. Ronald (Lokming) Lui.

He is a Croucher fellow (2024) and scholar (2019), and a Youde scholar (2018).

• email: siuc at stanford dot edu
• Google scholar
• CV

Scroll down for the Teaching, Mentorship, and Personal sections.

Research and Publications

Applied Topology

• The Topological Behavior of Preferential Attachment Graphs (Submitted)
  • C. Siu
  • (arxiv)
• Betti Numbers of Preferential Attachment Complexes (to appear in Advances in Applied Probability in Sep 2025)
  • C. Siu, G. Samorodnitsky, C. Yu, and R. He
  • (arxiv) (video)(poster) (slides) (codes)
• Detection of Small Holes by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtration
  • C. Siu, G. Samorodnitsky, C. Yu, and A. Yao
  • Journal of Applied and Computational Topology 2024
  • (doi)(arxiv) (video) (source codes) (poster for ATMCS 10) (slides)

Computational Geometry

• Decomposition of Longitudinal Deformations via Beltrami Descriptors
  • H. Law, C. Siu, and R. Lui.
  • Journal of Scientific Computing 2021
• Image Segmentation with Partial Convexity Shape Prior Using Discrete Conformality Structures
  • C. Siu, H.L. Chan, and R. Lui
  • SIAM Journal on Imaging Sciences 2020

Miscellaneous

• Geometry and Laplacian on Discrete Magic Carpets
  • C. Siu, and R. Strichartz (alphabetical order)
  • Journal of Fractal Geometry 2023
• An Elementary Approach on Left-Orderability, Cables of Torus Knots and Dehn Surgery
  • J. Li, and C. Siu (alphabetical order)
  • arxiv

Talks and Presentations

• Mar 23, 2024: Mid-Atlantic Topology Conference (poster), Northeastern University
  • “Topology of Scale-Free Complexes – Homology and Homotopy”
  • poster
• Mar 8, 2024: Data Science and Applied Topology Seminar (invited), City University of New York
  • “Homology and Homotopy Properties of Scale-Free Complexes”
  • slides
• Feb 16, 2024: Hot Topics in Data Science (invited), University at Buffalo
  • “Detecting Weak Topological Signals in Noisy Environments”
  • slides
• Feb 9, 2024: University of Florida Topological Data Analysis conference (invited). University of Florida
  • “Homology and Homotopy Properties of Scale-Free Networks”
  • slides
• Feb 9, 2023: Topology Seminar (invited), The Chinese University of Hong Kong
  • “Topological Data Analysis and Scale-Free Networks”
  • slides
• Dec 6, 2023: Topology Seminar (invited), The Chinese University of Hong Kong
  • “Topological Data Analysis and Scale-Free Networks”
  • slides
• Nov 17, 2023: Northeast Probability Seminar, New York University
  • “Asymptotics of Expected Betti Numbers of Preferential Attachment Clique Complexes”
  • slides
• Nov 12, 2023: Binghamton University Graduate Combinatorics, Algebra and Topology (BUGCAT 2023), Binghamton University
  • “Betti Numbers of Preferential Attachment Flag Complexes”
  • slides
• Nov 3, 2023: Applied Topology Seminar (invited; virtual), Oxford University
  • “The Expected Betti Numbers of Preferential Attachment Clique Complexes”.
  • slides
• Nov 1, 2023: Applied Algebraic Topology Research Network (AATRN) Online Seminar (invited; virtual)
  • “The Asymptotics of the Expected Betti Numbers of Preferential Attachment Clique Complexes”.
  • slides
• Sep 29, 2023: Computation Persistence Workshop
  • “The Asymptotics of the Expected Betti Numbers of Preferential Attachment Clique Complexes – Theory and Computational Challenges”.
  • slides
• Sep 27, 2023: Probability Seminar (invited), Purdue University
  • The Topology of Preferential Attachment Graphs
  • slides
• Sep 20, 2023: Seminario Doctorado, Actividad del Programa de Doctorado “Mathematicas” (invited), University of Seville
  • The Topology of Preferential Attachment
  • slides
• Sep 14, 2023: Probability and Applications Seminar (invited), Queen Mary University of London
  • The Topology of Preferential Attachment Graphs
  • slides
• Aug 6, 2023: Joint Statistics Meetings 2023
  • Discovery of Small Dense Topological Features from Dataset
  • slides
• Jun 8, 2023: Geometry and Topology meet Data Analysis and Machine Learning 2023
  • The Many Holes of Preferential Attachment”
  • slides
• Mar 22, 2023: Randomness in Topology and its Applications (IMSI workshop)
  • “Betti Numbers of Preferential Attachment Complexes” (poster).
  • poster
• Feb 26, 2023: Finger Lakes Probability Seminar
  • “Expected Betti Numbers of Preferential Attachment Complexes”
  • slides
• Nov 17, 2022: Morse Theory Seminar for Cornell Graduate Students
  • Introduction to Discrete Morse Theory
• Nov 6, 2022: Binghamton University Graduate Combinatorics, Algebra and Topology (BUGCAT 2022)
  • Detection of Small Cycles in Data by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtration
  • slides
• Oct 22, 2022: 3rd Upstate New York Topology Seminar (UNYTS 3)
  • Detection of Small Cycles in Data by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtration
  • slides
• Jun 20, 2022: Algebraic Topology: Methods, Computation and Science 10 (ATMCS 10)
  • Detection of Small Topological Features by the Scale-FInvariant Robust Density-Aware Distance (RDAD) Filtration (Poster)
  • poster
• Mar 8, 2022: Olivette Club
  • Topological Data Analysis: Klein Bottles and How Cornellians Find Them in Data
  • slides

Teaching

• MATH1920 Spring 2023
• MATH1920 Fall 2022
• MATH2020 Spring 2019
• EPYMT Number Theory and Cryptography, Summer 2018
• MATH4060 Fall 2018
• MATH2010 Spring 2018
• MATH1510 Spring 2018
• MATH1540 Fall 2017

Resources for Learning

• Dr. K. Delp’s unsolicited advice.
• Prof. I. Zakharevich’s homework guide.
• Prof. F. Su’s guidelines for good mathematical writing for lower-division students and upper division students
• D. Zemke’s tips on graph sketching
• G. Sanderson’s cool visualizations of calculus and linear algebra
• The Harvard Physics Department’s Guide to The Hidden Curriculum

Undergraduate Mentorship

If you are interested in doing an undergradate reading / research project, send me an email!

• Fall 2023 Avhan Misra on the topological behavior of preferential attachment graphs
• Fall 2022 Rongyi He on Preferential Attachment Models
• Fall 2021 Luis Hoderlein on Dimension Reduction and UMAP, and Category Theory of Mapper
• Fall 2021 Tom Shi on Ranking of Graph Data
• Spring 2021 Andrey Yao on Computational Topology II: From Persistent Homology to Ripser
• Fall 2020 Andrey Yao on Computational Topology: From Simplicial Complexes to Persistent Homology

Resources for Research

• Mathematical talks
  • How to Avoid Death by PowerPoint by D. Phillips
  • Tips compiled by Prof. D. Margalit
  • Why we choke under pressure – and how to avoid it by Prof. S. Beilock
• Mathematical writing
  • Writing a Math Phase Two Paper by Prof. S. Kleiman and its pdf version.
  • General Instructions for Final Draft of Short Paper by Prof. D. Kleitman
  • More tips compiled by Dr. E. Carberry
  • More tips compiled by Prof. D. Margalit
  • What other undergraduates wrote at Chicago and their Latex templates
  • LaTex Tutorials on Overleaf
  • Mathcha, a graphical interface for drawing Tikz diagrams
  • tikzcd-editor, a graphical interface for drawing commutative diagrams
• Coding skills
  • Some Stackexchange and Stack Overflow discussions on self-documenting codes, code reuse, unit testing, quality codes and the use of debuggers
  • The SOLID principles for writing clean codes
  • C. Williams’ introduction to functional programming
  • Beginners’ guide to programming on Reddit
• Coding tutorials
  • Dr. M. Lee’s Conda tutorial
  • Introduction to Github on Github
• Data management
  • Harvard LMA RDMWG’s tips for naming files
  • The FAIR principle
• Undergraduate Research Opportunities
  • at Williams
  • at Cornell
  • at Chicago (modify the link to see the most up-to-date page)
  • at Lawrence Berkeley National Lab
  • at MSRI
  • through many NSF-funded programs

Personal

I am from Hong Kong. I would be really happy if you greet me with “zou sun” and “ng on” (Good morning and Good afternoon in Cantonese).

My favorite author is Dostoyevsky; favorite TV show, Taskmaster. Need to balance the heaviness and the lightness.

I am mostly an indoor guy, but Ithaca has made me more active. Picked up hiking and ice-skating here. Try to catch me at a trail or in the rink.