ESP Biography

One of the most appealing aspects of modern mathematics is that many seemingly unrelated areas turn out to be closed related. One example of this underlying unity is the Euler characteristic, an integer invariant associated to many types of spaces, that appears in diverse areas of math like graph theory, topology, and geometry. We will first explore the seemingly innocent notion of the Euler characteristic of a graph and then explain why this integer is a "topological invariant." We will then connect the Euler characteristic to geometry and discuss the following interesting "weather" fact: there are always at least two points on the Earth where wind velocity is exactly zero (this would not be true if the Earth were the shape of a donut!).