Title: Polytopes and the Problem with Pick's Theorem

Date: 02/10/2017

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Polytopes are a generalization of convex polygons into higher dimensions. In two dimensions, we have Pick's Theorem: a simple way of relating the area of a polygon with the number of ordered pairs it contains where each coordinate is an integer. So, why not try to do the same thing with polytopes in general? Problems quickly arise, even in three dimensions. In this talk, I will describe what these problems are and how we can overcome them. The answers aren't obvious, but we will see just how much it pays off in the end.