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Seminar Details

Mutually Touching Infinite Cylinders and Ramsey Theory 

  • Start Date: November 10, 2025
  • Event Start Time: 2:00 PM
  • Event End Time: 3:00 PM
  • Seminar Series: Rutgers Discrete Mathematics Seminar
  • Presenter(s): Sammy Luo - Massachusetts Institute of Technology
  • Event Location: Conference Room 705 | Rutgers University | Hill Center | 110 Frelinghuysen Rd
  • Presentation Type: Stand Alone Presentation
  • Abstract:

    Littlewood asked for the maximum number $N$ of congruent infinite cylinders that can be arranged in $\mathbb{R}^3$ so that every pair touches. In this talk, we discuss the techniques behind some recent improvements on the upper bounds for this problem, culminating in our recent result showing that $N \leq 10$. Paired with a lower bound by Bozóki, Lee, and Rónyai, this establishes that $N \in \{7,8,9,10\}$. Our method is based on linear algebra and Ramsey theory, and makes partial use of computer verification.

    Based on joint work with Travis Dillon and Junnosuke Koizumi.