Graduate student colloquium

Jonathan Herman, Pure Mathematics, University of Waterloo

"The Curvature of Curves and Surfaces"

This talk will give an introduction to the differential geometry of  curves and surfaces. In particular, I will give precise meaning to the intuitive notion of a 'curved' surface or curve. We'll see how differential geometry extends notions from calculus to more abstract spaces; for example, it allows us to do calculus on a sphere, torus, catenoid and so on. From here, the goal will be to give a proof of Gauss's famous Thoerema Egregium.