Rupert Li
rupertli (at) stanford (dot) edu
About Me
I'm a PhD student at Stanford in the Department of Mathematics. My research interests include probability, combinatorics, and discrete geometry.
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. I then was a Part III student, receiving a MASt in Pure Mathematics from the University of Cambridge, at Trinity College, graduating with Distinction in 2025.
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.
Probability
- R. Li, Lampros Gavalakis, Ioannis Kontoyiannis. Entropic Additive Energy and Entropy Inequalities for Sums and Products. (arXiv)
- 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)
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)
Combinatorics
- Amogh Akella and R. Li. Diameter Bounds for Friends-and-Strangers Graphs. (arXiv)
- 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