EVENT DETAILS AND ABSTRACT

Title: Mirror symmetry and cluster algebras
Speaker: Paul Hacking
Speaker Info: UMass Amherst
Brief Description:
Special Note:
Abstract:

We interpret a Fomin-Zelevinsky cluster algebra as the ring of global functions on a non-compact Calabi-Yau variety obtained from a toric variety by a blowup construction. Motivated by mirror symmetry, we describe a canonical basis of a cluster algebra defined via tropical counts of holomorphic discs on the mirror, verifying conjectures of Fomin-Zelevinsky and Fock-Goncharov. This is joint work with Gross, Keel, and Kontsevich.