Title: Can arbitrarily many segments of a fixed length spin independently in the unit disk?
Speaker: Hannah Alpert (Ohio State University)
Abstract: The classical Kakeya needle problem asks, what is the infimal area of a region of the plane in which a unit segment can turn all the way around, perhaps translating as it does so? We can ask an analogous question for multiple segments in the unit disk. Can n segments of length r turn all the way around---that is, can they form the whole n-dimensional torus of possible angles---if they are allowed to translate as they turn? As n gets large, must r approach zero? This question comes from questions about the cohomology of the space of ways to arrange n disjoint disks of radius r in the unit disk.
Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html