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Sammy Luo - Mutually touching infinite cylinders and Ramsey theory
Location: Hill 705
Date & time: Monday, 10 November 2025 at 2:00PM - 3:00PM
Speaker: Sammy Luo (MIT)
Title: Mutually touching infinite cylinders and Ramsey theory
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.