Seminars & Colloquia Calendar
Deformations of the moduli space of polygons
Marco Castronovo, Rutgers University
Location: Hill 705
Date & time: Thursday, 25 January 2018 at 11:00AM - 11:45AM
Abstract: We construct a Kähler moduli space parametrizing polygons in R^3 with given side lengths. A path in the positive cone of lengths gives a deformation of the moduli of polygons, which changes topology at some critical times. Along a canonical path, this deformation matches the Kähler-Ricci flow. Specialising to moduli spaces of pentagons, we explain why they are generically toric del Pezzo surfaces and describe natural Lagrangian tori in them. Some open Gromov-Witten invariants of these tori are encoded by a Laurent polynomial called disk potential, and we show how to compute it in practice. Finally, we highlight some open questions regarding the disk potential and their connection with Kontsevich's homological mirror symmetry.