Fabian Haiden - Legendrian skein algebras and Hall algebras
This is a report on work in progress in understanding the relation between skein algebras and Hall algebras of Fukaya categories, motivated by a recent paper of Cooper-Samuelson. Another motivation is the problem of defining Hall algebras for Z/2-graded categories, and the limiting case q=1. The main novelty is to assign to a Lagrangian submanifold a positive linear combination of isomorphism classes of objects in the Fukaya category (i.e. a “random object”).