Objectives:

Geometric Transversal Theory has long become a major area of Discrete Geometry, with strong connections to Linear Optimization and Algebraic Topology. The work on Helly-type Theorems led to deep quantitative problems whose study was spearheaded by Alon, Barany, Goodman, Pollack, Kalai, Katchalski, Kleitman, Lovasz, Wenger, and others. As has been discovered in late 1980s, the answers to several of these questions essentially rely on the existence of small-size Epsilon-nets.

The study of Epsilon-nets is related to a number of deep notions including Tverberg-type and geometric selection theorems, and hypergraph containers. In the past 10 years, significant advances and far-reaching generalizations in this connection have been done by Alon, Balogh and Solymosi, Pach and Tardos, Aronov, Ezra and Sharir, Bukh, Matoušek, and Nivasch, Gromov, Karasev, Wagner, and many others.

In the same time, we have witnessed remarkable progress by Fox, Pach, Suk, Toth, and others towards the closely related goal of understanding the Ramsey-theoretic properties of the graphs and hypergraphs that arise in combinatorial geometry (e.g., semi-algebraic hypergraphs, and graphs that represent intersections among Jordan arcs or convex sets).

We ask to capitalize on this momentum by bringing together researchers in such aspects of combinatorial geometry as Helly-type Theorems and transversal numbers of families of convex sets, Epsilon-nets, and geometric Ramsey-type and regularity theorems.

This is a second meeting which is organized as part of the 5-year project Combinatorial Aspects of Computational Geometry supported by the European Research Council (ERC).

The program begins on Sunday, January 27, 2019, when a bus/shuttle will leave Tel Aviv/Ben-Gurion Airport to spectacular Ein-Gedi resort, in close proximity to the Dead Sea and the famous Ein-Gedi natural reserve. The scientific part of the conference stretches over 4.5 days filled with talks, working sessions, and a local excursion. The program ends on Thursday afternoon when the participants will be taken back to Tel Aviv and/or Ben-Gurion Airport.