The Homfly skein and elliptic Hall algebras
- Series
- Geometry Topology Seminar
- Time
- Wednesday, November 30, 2016 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Peter Samuelson – Edinburgh – petersamuelson@gmail.com
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.)