Project by Kira Adaricheva
We will investigate discrete structures known as convex geometries. These structures appear in many different parts of mathematics. In this project, we will focus on convex geometries generated by a classical convex hull operator acting on finite sets of points, circles, ellipses, or different types of shapes. These could be located on a plane, a 3-dimensional space, or higher dimensional spaces.
​
A good starting points for reading about convex geometries is
-
P. Edelman, R. Jamison, The theory of convex geometries, Geom.Dedicata 19(3), 1985, 247-270.
​
A paper on the subject from a previous undergraduate project mentored by Kira:​
-
K. Adaricheva, M. Bolat, Representation of convex geometries by circles on the plane, Discrete Mathematics, 342(2019), 726-746.
​
There are three open problems listed in Section 7 of this paper. Some of those were already studied after the paper appeared in 2016. But there are more related questions, which could be offered to interested individuals, when they familiarize themselves with the background.