TL;DR
This paper explores Helly-type theorems, highlighting their key principles and themes at the intersection of combinatorics and geometry, and discusses various related problems.
Contribution
It provides an overview of Helly-type theorems, outlining main themes and presenting open problems in the field.
Findings
Identification of core themes in Helly-type theorems
Connection between combinatorics and geometry in these theorems
Presentation of open problems and research directions
Abstract
In this paper, we present a variety of problems in the interface between combinatorics and geometry around the theorems of Helly, Radon, Carath\'eodory, and Tverberg. Through these problems we describe the fascinating area of Helly-type theorems, and explain some of its main themes and goals.
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