Video URL
https://pirsa.org/17040075Cluster duality and mirror symmetry for Grassmannians
APA
Williams, L. (2017). Cluster duality and mirror symmetry for Grassmannians. Perimeter Institute for Theoretical Physics. https://pirsa.org/17040075
MLA
Williams, Lauren. Cluster duality and mirror symmetry for Grassmannians. Perimeter Institute for Theoretical Physics, Jun. 12, 2017, https://pirsa.org/17040075
BibTex
@misc{ scivideos_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 for Theoretical Physics}, year = {2017}, month = {jun}, note = {PIRSA:17040075 see, \url{https://scivideos.org/pirsa/17040075}} }
Lauren Williams University of California, Berkeley
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.