Geometry and Topology Seminar

The Homfly skein relations from knot theory can be used to associate an algebra to each (topological) surface. The Hall algebra construction associates an algebra to each smooth (algebraic) curve over a finite field. Using work of Burban and Schiffmann, we show that the skein algebra of the torus is isomorphic to the Hall algebra of an elliptic curve. If time permits we discuss a third (categorical) construction of the same algebra. (Joint with Morton and Licata.)