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.