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                * Princeton Discrete Math Seminar *
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Speaker: Sammy Luo (MIT)

Thursday 5th February, 3:00 in Fine Hall 224.

Title: Mutually touching infinite cylinders and Ramsey theory

Littlewood asked for the maximum number N of congruent infinite cylinders that
can be arranged in 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 is 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.

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