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I am a fourth-year Ph.D. student in Mathematics at UC Berkeley, advised by Prof. Venkatesan Guruswami. Previously, I graduated from Stanford University with a Bachelor’s degree in Mathematics with honors and a concurrent Master’s degree in Computer Science (AI track).

My research interests lie broadly in Error-Correcting Codes, Automated Theorem Proving, and Machine Learning.

Selected Publications

FRgraph

Density Frankl–Rödl on the Sphere

Generalizes the Frankl–Rödl theorem to the sphere by proving a density statement for spherical avoidance problems; further establishes that all simplices are sphere Ramsey.
* Equal contribution. Authors listed alphabetically.
Sidon set

A Deterministic Construction of a Large Distance Code from the Wozencraft Ensemble

Venkatesan Guruswami*, Shilun Li* IEEE Transactions on Information Theory | [Paper]
(Presented at RANDOM 2023)
Applies Sidon sets to code construction (the first such application) and presents the first explicit construction of rate-1/2 Wozencraft codes with Ω(√k) minimum distance.
* Equal contribution. Authors listed alphabetically.
Coin toss

Dynamics and Probability in the Toss of a Coin with Symmetric Inhomogeneous Density

Shilun Li Preprint | [Paper]
Proves that coin tosses are biased — coins favor the starting face — and extends Diaconis's probability formula to general biased coins.

Experience

  • Machine Learning Intern, Apple Inc. (Cupertino, CA), 01/2026 – 07/2026
  • Advisor/Lecturer, XAcademy (Shanghai, China), 07/2023 – 08/2023 & 07/2025 – 08/2025
  • Research Collaborator, Microsoft Research (Mountain View, CA), 05/2024 – 01/2025
  • Co-founder, FutureX / Futurexyz Co. (Palo Alto, CA), 05/2022 – 05/2023
  • AI Developer Intern, Tencent (Shenzhen, China), 06/2021 – 09/2021
  • Research Assistant, Stanford Mathematics (advised by Prof. Rafe Mazzeo), 06/2021 – 06/2022
  • Research Assistant, Stanford Vision and Learning Lab (advised by Prof. Fei-Fei Li), 06/2020 – 10/2020
  • Software Engineer Intern, Convertlab (Shanghai, China), 11/2020 – 01/2021
  • Research Assistant, Stanford NLP Group (advised by Prof. Christopher Manning), 06/2019 – 09/2019

Awards & Distinctions

  • McBeth Family Fellowship in Mathematics, UC Berkeley — 2025

  • Departmental Honors in Mathematics, Stanford University — 2022 (Awarded to top 15% of graduating cohort.)

  • Top Three Projects, Stanford BIOME Biohackathon — 2018

  • AMS Special Award, Intel ISEF — 2017 (The world’s largest pre-college STEM competition.)

  • National Best High School Student, All-China Students’ Federation — 2017 (Top 10 out of 170,000 nationwide.)

  • First Prize (Two-time), Provincial Science & Technology Innovation Contest — 2016 (Top 5 out of 400 in the province.)

  • Gold Award in Science & Gold Award in Math, S.-T. Yau Science Award — 2016 (1st out of 5,800+ global participants.)

Education

UC Berkeley — Ph.D. in Mathematics (Aug 2022 – Jun 2027, expected) GPA: 4.0/4.0 · Advised by Venkatesan Guruswami

Stanford University — M.S. in Computer Science (AI track) (Sep 2019 – Jul 2022) GPA: 4.0/4.0

Stanford University — B.S. in Mathematics with Honors (Sep 2018 – Jul 2022) GPA: 4.0/4.0 · Advised by Rafe Mazzeo