Balázs Keszegh: The number of tangencies between two families of curves

Description of video

Date: 5/13/22
Speaker :Keszegh Balázs

We prove that the number of tangencies between the members of two families, each of which consists of n pairwise disjoint curves, can be as large as Ω(n4/3). From a conjecture about 0-1 matrices it would follow that if the families are doubly-grounded then this bound is sharp. We also show that if the curves are required to be x-monotone, then the maximum number of tangencies is Θ(nlogn), which improves a result by Pach, Suk, and Treml. Joint work with Dömötör Pálvölgyi.