Problems in Discrete Geometry and Extremal Combinatorics
In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.
We study several problems in discrete geometry and extremal combinatorics. Discrete geometry studies the combinatorial properties of finite sets of simple geometric objects. One theme of the field is geometric Ramsey theory. Given m geometric objects, we want to select a not too small subset forming a configuration that is “regular” in some sense.