PIRSA:17040075

Cluster duality and mirror symmetry for Grassmannians

Williams, L. (2017). Cluster duality and mirror symmetry for Grassmannians. Perimeter Institute. https://pirsa.org/17040075

Williams, Lauren. Cluster duality and mirror symmetry for Grassmannians. Perimeter Institute, Jun. 12, 2017, https://pirsa.org/17040075 

          @misc{ pirsa_PIRSA:17040075,
            doi = {10.48660/17040075},
            url = {https://pirsa.org/17040075},
            author = {Williams, Lauren},
            keywords = {Mathematical physics},
            language = {en},
            title = {Cluster duality and mirror symmetry for Grassmannians},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {jun},
            note = {PIRSA:17040075 see, \url{https://pirsa.org}}
          }

Lauren Williams University of California, Berkeley

DOI 10.48660/17040075
Collection
Talk Type Scientific Series
Subject

Abstract

We use the cluster structure on the Grassmannian and the combinatorics of plabic graphs to exhibit a new aspect of mirror symmetry for Grassmannians in terms of polytopes. From a given plabic graph G we have two coordinate systems: we have a network chart for the A-model Grassmannian, and a cluster chart for the B-model (Landau-Ginzburg model) Grassmannian. On the A-model side, we use the network chart from G and an ample divisor D to define an associated Newton-Okounkov polytope NO_G(D). We give explicit formulas for the lattice points in NO_G(D) in terms of the combinatorics of Young diagrams.   We then reinterpret NO_G(D) in terms of the superpotential and the cluster chart for the B- model Grassmannian. *This is joint work with Konstanze Rietsch.