Yao-Rui's Webpage (?)

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4C15 David Rittenhouse Laboratory
yeya [at] math [dot] upenn [dot] edu

About Me

I was a math graduate student at the University of Pennsylvania (graduated May 2021), and will be moving to NYU.

I am broadly interested in special functions arising from number theory. I also study applications of special functions to combinatorics, physics, and biology.

Outside math, I am involved in piano performances and transcriptions. I was a member of Penn Chamber.

Teaching and Tutoring

I am available for tutoring in math and music if you currently aren't a student in my class; email me if interested.

• Spring 2021: MATH 603 (Algebra).
• Spring 2021: Directed Reading Program (The Fifteen Theorem).
• Fall 2020: AMCS 602 (Applied Algebra).
• Fall 2020: Directed Reading Program (Flow Modeling and Car Accident Risk).
• Spring 2020: Directed Reading Program (Finite Fields and Cryptography).
• Summer 2019: MATH 240 (Calculus, Part III). Lecture Notes
• Spring 2019: MATH 241 (Calculus, Part IV). Homework Solutions (with Iyer Pranav)
• Fall 2018: MATH 420 (Ordinary Differential Equations).
• Spring 2018: MATH 240 (Calculus, Part III).
• Fall 2017: MATH 371 (Algebra).
• Fall 2017: MATH 110 (Calculus for Wharton Students).

Journal Articles

• Algebraic independence results for colored multizeta values in characteristic $p$. Draft available upon request.
• Towards analytical calculation of the magnetic flux measured by magnetometers (with Wan-Jin Yeo and Samu Taulu). Physics Letters A. Link
• A computational model for estimating the progression of coronavirus cases in the US West and East Coast population regions (with Yao-Yu Yeo and Wan-Jin Yeo). Experimental Results. Link
• Branching rules for splint root systems (with Logan Crew and Alexandre A. Kirillov). Algebras and Representation Theory. Link
• Enumerating $(k,l)$-critical and supercritical permutations (with Wan-Jin Yeo). Mathematical Medley.

Other Articles

• Mixed Carlitz motives and colored multizeta values in characteristic $p$. PhD Thesis.
• Dessin d'enfants and superpotentials. Honors Thesis.

Notes

Here are my oral exam transcript and oral exam practice problems.

Here is a collection of fun short puzzles (compiled with Alon Benhaim), best suited to mull over coffee break.

Here are some notes for various mathematical events.

• Multizeta values in characteristic $p$. Notes
• $\mathbb{F}_q[\theta]$ is level; $\zeta$ is you; $Li$ is win. Notes
• Jacobi polynomials via pictures. Notes
• Music 101 for science people. Notes
• Branching rules for splint root systems. Notes
• Adelic class groups via two quick examples. Notes
• Examples of spectral sequences (with Man Cheung Tsui). Notes
• Counting genera of integral quadratic forms. Notes
• Congruent numbers. Notes
• Bhargava's cube. Notes
• MSRI summer school: Automorphic forms and the Langlands program (Lectures by Kevin Buzzard). Notes
• The Banach-Tarski paradox. Notes
• The 15 and 290 theorems. Notes
• Sum of squares. Notes
• Little tidbits about the symmetric group. Notes
• Dessin d'enfants and superpotentials. Notes
• The Hurwitz existence problem. Notes