Winston Cheong

• Email: cheong.winston1337 at gmail dot com
• Affiliation: Rowan University. cheong94 [at] rowan [dot] edu

Table of Contents

• Winston Cheong
• Table of Contents
• Education
• Awards
• Research interests
  • Current
  • During Undergrad
• Publications and Preprints
• Presentations
• Possibly useful things
• Some seminar pages
• Teaching
• For graduate students / enterprising undergrads
  • Suggested reading
  • LaTeX
  • People with good notes
  • A tip on how to use researchseminars.org:

Education

• Masters in Mathematics, Kansas State Univeristy (2020)
• Bachelors of Science in Mathematics, Rowan University (2016)
• Bachelors of Science in Computer Science, Rowan University (2016)

Awards

• Dean's Outstanding Senior Awards (2016)
• College of Science and Mathematics STEM Excellence in Research Award (2014)

Research interests

Current

• Autoformalization
• Derived algebraic geometry
• "Perfection"
• Mirror symmetry
• Langlands program
• Formalization of mathematics, e.g.:
  • Perfectoid spaces (1910.12320)
  • $\infty$-categorical Yoneda lemma (2309.08340)
• Using machine learning to aid in discovering new mathematics
• Physical Mathematics

During Undergrad

• Ramanujan-style number theory (e.g. partition function, mock theta functions / mock modular forms)
• proof of Fermat's last theorem
• the modularity theorem
• Langlands program
• (Monstrous/Mathieu/Umbral) moonshine
• Quantum topology
• Categorification

Publications and Preprints

1. Winston Cheong, Alexander Doser, McKinley Gray, and Stephen F. Sawin. "Relationship of the Hennings and Witten-Reshetikhin-Turaev invariants for higher rank quantum groups." J. Knot Theory and Ramifications 2023 32:07. https://doi.org/10.1142/S0218216523500487 Preprint version: arXiv:1701.01423
2. Daniel Bittner, Long Cheong, Dante Gates, and Hieu Nguyen. "New Approximations for the Area of the Mandelbrot Set." Involve, a Journal of Mathematics 10, no. 4 (March 7, 2017): 555–572. https://doi.org/10.2140/involve.2017.10.555. Preprint version: arXiv:1410.1212
3. Hieu D. Nguyen and Long G. Cheong. "New Convolution Identities for Hypergeometric Bernoulli Polynomials." Journal of Number Theory 137 (April 1, 2014): 201–221. https://doi.org/10.1016/j.jnt.2013.11.008. Preprint version: arXiv:1401.2970

Presentations

1. 2016 JMM poster session - "Relationship of the Hennings and Chern-Simons Invariant for Higher Rank Quantum Groups"
2. 2015 Oct 26 - "The Hennings and Chern-Simons Witten Three-Manifold Invariants" (Rowan Mathematics Department Colloquium Series)
3. 2015 Summer - "REU Topic: Invariants of 3-manifolds" slides
4. 2014 Rowan STEM Symposium - Poster presentation "Converging on the Area of the Mandelbrot Set"
5. 2013 Nov 20 - "Converging on the Area of the Mandelbrot set" (Rowan Mathematics Department Colloquium Series, joint presentation with Daniel Bittner) slides

Possibly useful things

• Verdier's thesis (converted over from the ps files here)
• translation of Lefevre-Hasegawa's thesis
• Interactive math utilities by Pieter Belmans (Github profile):
  • https://www.fanography.info/
  • https://www.grassmannian.info/
  • https://www.hyperkaehler.info/
  • https://superficie.info/#input
  • http://pbelmans.ncag.info/cohomology-tables/
• Adjectives Project
• Better KSU Math Exam Archive

Some seminar pages

• M-seminar, youtube channel
• WHCGP seminar
• Informal string math seminar
• Paris algebra seminar
• BunG seminar, their YT

Teaching

• 2023 Fall : Calc 1
• 2023 Summer : Calc 3
• 2023 Spring : Calc 2
• 2022 Fall : Calc 3
• 2022 Spring : Trig
• 2020 Spring : Calc 1
• 2019 Fall : Calc 1

For graduate students / enterprising undergrads

Suggested reading

• Thurston's On Proof and Progress in Mathematics
• Vakil's "Three Things" exercise, for getting things out of talks/talks. See also his advice for students
• Terence Tao's blog posts:
  • There's more to mathematics than rigour and proofs
  • Write down what you've done
  • Work hard
• Atiyah's "Mathematics in the 20th Century" article.
• Ben Webster's Geometry and categorification
• Emily Riehl's Infinity category theory from scratch (arxiv version)
• Periodicals
  • Quanta Magazine
  • Notices of the AMS
  • Bulletin of the AMS
  • ICM Proceedings

LaTeX

People with good notes

• Evan Chen
  • Napkin project
  • MIT 18.02 (Multivariable Calculus)
• J.S. Milne
• Arun Debray
• William (W.W.L.) Chen (analytic number theory, discrepancy theory)
• David Mehrle
• Zev Chonoles
• Peter Haine
• Daniel (Dani) Tubbenhauer

A tip on how to use researchseminars.org:

1. Create an account
2. Subscribe / Favorite the seminars you're interested in
3. Import your automatically-managed user calendar to your calendar-ing app of choice (scroll to the bottom of https://researchseminars.org/user/info)