This seminar runs every Monday during the semester at 2PM in Hill 705. The current organizers are Jeff Kahn, Bhargav Narayanan, Swee Hong Chan, and Natalya Ter-Saakov.
If you wish to join our listserv, please email Natalya Ter-Saakov at nt399@math.rutgers.edu.
Click here for the abstract archive for this semester, and here for older abstracts.
Next Talk:
Date: November 10, 2025 at 2:00pm
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.
November 10 --- Sammy Luo (MIT)
November 17 --- Special Colloquium
December 1 --- Daniel Zhu (Princeton)