|Date: Friday, March 27, 2015
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: The symplectic double and F-polynomials
Abstract: The symplectic double is an algebraic variety introduced by Fock and Goncharov as part of their work on quantization of cluster varieties. This variety is defined using the mutation formulas from the theory of cluster algebras with a particular choice of semifield. The positive real points of the symplectic double can be identified with a certain Teichmuller space, and there is a tropicalization of the symplectic double which can be identified with a certain space of laminations. I will explain both of these constructions precisely and describe a canonical pairing between the Teichmuller and lamination spaces. I will give an explicit formula for this pairing using the F-polynomials of Fomin and Zelevinsky.
Speaker: Dylan Allegretti
Institution: Yale U.