Spinning doughnuts and other symmetries of surfaces

Abstract:

This talk is about surfaces, which are two-dimensional shapes. We will look at a number of surfaces, including the sphere and the torus, which is the surface of a doughnut. We can build new surfaces by gluing together old ones and use this technique to describe all surfaces. 
What happens if we incorporate symmetry? Surfaces have many symmetries, for example we can reflect across the equator of the sphere or spin a doughnut.  We will look at recent work classifying surfaces together with their symmetries, as well as some of my own work studying their invariants.