Algebraic & Arithmetic Geometry Seminar: "Reconciling mutations for Fano and cluster varieties"

Speaker: Ben Wormleighton, Washington University in Saint Louis

Abstract: This is a report on joint work with Jonathan Lai and Tim Magee. I will describe a precise, explicit comparison between mirror symmetry constructions for orbifold del Pezzo surfaces coming from the Fanosearch program and for log Calabi--Yau pairs coming from the Gross--Hacking--Keel theory of cluster varieties. In particular, we identify polytopes found via scattering diagrams with Fano polytopes of toric degenerations. In many cases, our methods also recover Landau-Ginzburg models associated to toric degenerations in cluster-theoretic terms.

Host: Matt Kerr