Winston Cheong

• Email: cheong.winston1337 at gmail dot com

Table of Contents

• Winston Cheong
• Table of Contents
• Research interests
  • Current
  • During Undergrad
• Publications and Preprints
• Presentations
• Possibly useful things
• Teaching
• For Graduate students
  • A tip on how to use researchseminars.org:

Research interests

Current

• 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:
  • 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

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

• Suggested reading for starting grad students:

  • 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
  • Evan Chen's Napkin project

• For breadth, read (but don't overdo):

  • Quanta Magazine
  • Notices of the AMS
  • Bulletin of the AMS
  • ICM Proceedings

• Become proficient in LaTeX

  • My info on LaTeX

• People with good notes:

  • Evan Chen
  • J.S. Milne
  • Arun Debray
  • 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)