Speaker
Andrey Myatelin
(Moscow Institute of Physics and Technology)
Description
A finite family $\mathcal{F}$ of convex sets is called satisfying $(p,q)$-property or just a $(p,q)$-family if among any $p$ members of this family there are $q$ of them having a point in common. It is known that if $p \leq q \leq d+1$ then there is a constant $HD_d(p,q)$ such that for any $(p,q)$-family $\mathcal{F}$ of convex sets in $\mathbb{R}^d$ there is a set of $HD_d(p,q)$ points that intersects every member of $\mathcal{F}$. The goal of our work is finding new upper bound on $HD_2(4,3)$. During the presentation it will be told about current progress on initial problem and our results related to properties of $(4,3)$-families of convex sets on a plane.
Primary author
Andrey Myatelin
(Moscow Institute of Physics and Technology)
