Newton-Okounkov bodies for Grassmannians | Vidéo | Carmin.tv

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Newton-Okounkov bodies for Grassmannians

By Lauren Williams

Appears in collections : Cluster algebras: twenty years on / Vingt ans d'algèbres amassées, Exposés de recherche

In joint work with Konstanze Rietsch (arXiv:1712.00447), we use the $\mathcal{X}$-cluster structure on the Grassmannian and the combinatorics of plabic graphs to associate a Newton-Okounkov body to each $\mathcal{X}$-cluster. This gives, for each $\mathcal{X}$-cluster, a toric degeneration of the Grassmannian. We also describe the Newton-Okounkov bodies quite explicitly: we show that their facets can be read off from $\mathcal{A}$-cluster expansions of the superpotential. And we give a combinatorial formula for the lattice points of the Newton-Okounkov bodies, which has a surprising interpretation in terms of quantum Schubert calculus.

Information about the video

Date of recording 21/03/2018
Date of publication 28/03/2018
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19384003
Cite this video Williams, Lauren (21/03/2018). Newton-Okounkov bodies for Grassmannians. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19384003
URL https://dx.doi.org/10.24350/CIRM.V.19384003

Domain(s)

Bibliography

Rietsch, K., & Williams, L. (2017). Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians. <arXiv:1712.00447> - https://arxiv.org/abs/1712.00447

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