|Computer Science/Discrete Mathematics Seminar I|
|Topic:||An Application of the Universality Theorem for Tverberg Partitions|
|Affiliation:||Renyi Institute, Hungary and UCL, London|
|Date:||Monday, March 18|
|Time/Room:||11:00am - 12:00pm/Simonyi Hall 101|
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.