Noetherian Ring Seminar Winter 2013

February 7, 2013

Isoperimetric Inequalities

Ellen Veomett, Saint Mary's College of California, Mathematics and Computer Science Department

In this talk, we will consider various types of isoperimetric inequalities. We'll discuss the Brunn-Minkowski Theorem and use it to prove the Euclidean isoperimetric inequality. We will then move on to graphs and examine how the technique of compression can be used to prove Harper's Theorem, a discrete isoperimetric inequality on the boolean cube. We'll look at other isoperimetric inequalities on graphs, including some recent results for a family of graphs on Z^n.