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Cluster duality and mirror symmetry for the Grassmannian

Hot Topics: Cluster algebras and wall-crossing March 28, 2016 - April 01, 2016

March 31, 2016 (02:30 PM PDT - 03:30 PM PDT)
Speaker(s): Lauren Williams (University of California, Berkeley)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • B-model

  • algebraic combinatorics

  • Grassmannians and cell decompositions

  • cluster algebras

  • mirror symmetry

  • polytope theory

  • Plucker coordinates

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14488

Abstract

In joint work with Konstanze Rietsch, 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 positive chart for our A-model Grassmannian, and we have a cluster chart for our B-model (Landau-Ginzburg model) Grassmannian. On the A-model side, we use the positive chart to associate a corresponding Newton-Okounkov (A-model) polytope. On the B-model side, we use the cluster chart to express the superpotential as a Laurent polynomial, and by tropicalizing this expression, we obtain a B-model polytope. Our main result is that these two polytopes coincide

Supplements
25696?type=thumb L. Williams 375 KB application/pdf Download
Video/Audio Files

14488

H.264 Video 14488.mp4 362 MB video/mp4 rtsp://videos.msri.org/data/000/025/639/original/14488.mp4 Download
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