An Application of the Universality Theorem for Tverberg Partitions

Computer Science/Discrete Mathematics Seminar I
Topic:An Application of the Universality Theorem for Tverberg Partitions
Speaker:Imre Barany
Affiliation:Renyi Institute, Hungary and UCL, London
Date:Monday, March 18
Time/Room:11:00am - 12:00pm/Simonyi Hall 101
Video Link:https://video.ias.edu/csdm/2019/0318-ImreBarany

We show that, as a consequence of a remarkable new result of Attila P\'or on universal Tverberg partitions, any large-enough set $P$ of points in $\Re^d$ has a $(d+2)$-sized subset whose Radon point has half-space depth at least $c_d \cdot |P|$, where $c_d \in (0, 1)$ depends only on $d$. We then give an application of this result to computing weak $\eps$-nets by random sampling. Joint work with Nabil Mustafa.