The Gauss Bonnet Theorem
Patrick Boland, Ph.D.
University of Michigan
The geometry of surfaces is a classical topic in mathematics. During the nineteenth century, a beautiful formula relating the curvature (a geometric notion) and the genus (a topological notion) of a surface was discovered. This Gauss Bonnet theorem has become a prototype for a wide variety of formulas that relate seemingly disparate areas of math. The talk will introduce the Euler characteristic and curvature of a surface in three dimensional space. We will discuss the Gauss Bonnet theorem in the context of several examples and outline a proof of the formula.
As time permits, we will talk about applications and generalizations of the theorem.
Patrick Boland is a 2003 graduate from Providence College. He obtained a Ph.D. in mathematics from the University of Massachusetts in 2010. He has been affiliated with the University of Michigan for the last three years as a postdoctoral researcher. His main research areas are geometry and topology.
