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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 Coding Theory, 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