Hall algebras and the Fukaya category

Triangle Topology Seminar

Peter Samuelson (University of Edinburgh)

Tuesday, October 10, 2017 -
4:30pm to 5:30pm
at UNC

The Hall algebra is an invariant of an abelian (or triangulated) category C whose multiplication comes from "counting extensions in C." Recently, Burban and Schiffmann defined the "elliptic Hall algebra" using coherent sheaves over an elliptic curve, and this algebra has found applications in knot theory, mathematical physics, combinatorics, and more. In this talk we discuss some background and then give a conjectural description of the Hall algebra of the Fukaya category of a topological surface. This is partially motivated by an isomorphism between the elliptic Hall algebra and the skein algebra of the torus, which we also discuss. (Joint works with H. Morton and with B. Cooper.)

Last updated: 2017/09/25 - 10:06am