Rupert Li

rml61 (at) cam (dot) ac (dot) uk

About Me

I graduated from MIT in 2024 as a double major S.B. in Mathematics (course 18) and Computer Science, Economics, and Data Science (course 6-14) with a M.Eng. in Computer Science, Economics, and Data Science. During AY 2024-2025 I'm a Part III student, i.e., pursuing a MASt in Pure Mathematics from the University of Cambridge, at Trinity College. I will begin my PhD at Stanford in the Department of Mathematics in 2025.

My research interests include probability, combinatorics, and discrete geometry.

Selected Works

  • R. Li. Dual Linear Programming Bounds for Sphere Packing via Discrete Reductions. Advances in Mathematics, 460:110043 (2024). (arXiv) (journal)
  • Colin Defant and R. Li. Ungarian Markov Chains. Electronic Journal of Probability, 28:1-39 (2023). (arXiv) (journal)
  • Colin Defant, R. Li, James Propp, Benjamin Young. Tilings of Benzels via the Abacus Bijection, Combinatorial Theory, 3(2):1-24 (2023). (arXiv) (journal)

    • Research

    An up-to-date list of my papers, in reverse-chronological order, can be found on the arXiv.

    Discrete Geometry

  • R. Li. Dual Linear Programming Bounds for Sphere Packing via Discrete Reductions. Advances in Mathematics, 460:110043 (2024). (arXiv) (journal)
  • R. Li. Unique Optima of the Delsarte Linear Program. Designs, Codes and Cryptography, 91:2117-2140 (2023). (arXiv) (journal)

    • Probability

  • R. Li, Elchanan Mossel. Noise Sensitivity of Hierarchical Functions and Deep Learning Lower Bounds in General Product Measures. (arXiv)
  • R. Li, Elchanan Mossel, Benjamin Weiss. Monotonicity, Topology, and Convexity of Recurrence in Random Walks. (arXiv)
  • Colin Defant and R. Li. Ungarian Markov Chains. Electronic Journal of Probability, 28:1-39 (2023). (arXiv) (journal)
  • Colin Defant, R. Li, Evita Nestoridi. Rowmotion Markov Chains. Advances in Applied Mathematics, 155:102666 (2024). (arXiv) (journal)

    • Combinatorics

  • Neil Krishnan and R. Li. On the Connectivity of Friends-and-strangers Graphs. (arXiv)
  • Colin Defant, Leigh Foster, R. Li, James Propp, Benjamin Young. Tilings of Benzels via Generalized Compression, SIAM Journal on Discrete Mathematics, 39(1):146-162 (2025). (arXiv) (journal)
  • Colin Defant, R. Li, James Propp, Benjamin Young. Tilings of Benzels via the Abacus Bijection, Combinatorial Theory, 3(2):1-24 (2023). (arXiv) (journal)
  • Letong Hong and R. Li. Length-Four Pattern Avoidance in Inversion Sequences. Electronic Journal of Combinatorics, 29(4):37 (2022). (arXiv) (journal)
  • R. Li. Vincular Pattern Avoidance on Cyclic Permutations. Enumerative Combinatorics and Applications, 2(4):PP3 (2022). (arXiv) (journal)
  • R. Li. The Spum and Sum-diameter of Graphs: Labelings of Sum Graphs. Discrete Mathematics, 345(5):112806 (2022). (arXiv) (journal)
  • R. Li and James Propp. A Greedy Chip-firing Game. Random Structures & Algorithms, 62(3):645-666 (2023). (arXiv) (journal)
  • Yibo Gao and R. Li. Compatible Recurrent Identities of the Sandpile Group and Maximal Stable Configurations. Discrete Applied Mathematics, 288:123-137 (2021). (arXiv) (journal)

    • Curriculum Vitae

    A complete CV or resume is available upon request.

    Selected awards

  • 2025 PD Soros Fellow
  • 2024 Hertz Fellow
  • 2024 Marshall Scholar
  • Honorable Mention, 2023 Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student
  • 2023 Barry Goldwater Scholar
  • 2020 Regeneron Science Talent Search Fourth Place Winner