Convex holes in high-dimensional point sets

Abstract: It is well-known that every large enough set P in an Euclidean space contains k points in convex position. Such k points are called "hole" if their convex hull contains no other point of P. We present a new construction of k-hole-free sets in high-dimensional spaces. Surprisingly, the construction is based on non-trivial low-discrepancy sequences used for numerical integration. Joint work with Ting-Wei Chao and Ron Holzman.

combinatoricsprobability

Audience: researchers in the topic

Extremal and probabilistic combinatorics webinar

Series comments: We've added a password: concatenate the 6 first prime numbers (hence obtaining an 8-digit password).