The Homfly skein and elliptic Hall algebras

Geometry Topology Seminar
Wednesday, November 30, 2016 - 3:00pm
1 hour (actually 50 minutes)
Skiles 006
The Homfly skein algebra of a surface is defined using links in thickened surfaces modulo local "skein" relations. It was shown by Turaev that this quantizes the Goldman symplectic structure on the character varieties of the surface. In this talk we give a complete description of this algebra for the torus. We also show it is isomorphic to the elliptic Hall algebra of Burban and Schiffmann, which is an algebra whose elements are (formal sums of) sheaves on an elliptic curve, with multiplication defined by counting extensions of such sheaves. (Joint work with H. Morton.)