POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS
Name
1806.05307.pdf
Description
Submitted version
Size
1.41 MB
Format
Adobe PDF
Checksum (MD5)
1afe6a171c625c6368af19c8191cd7e2
Author(s)
POSTNIKOV, ALEXANDER
Date Issued
May 2019
Journal
Proceedings of the International Congress of Mathematicians, ICM 2018
Publisher
WORLD SCIENTIFIC
Citation
POSTNIKOV, ALEXANDER. 2019. "POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS." Proceedings of the International Congress of Mathematicians, ICM 2018, 4.
Version
Original manuscript
Abstract
© ICM 2018.All rights reserved. The nonnegative Grassmannian is a cell complex with rich geometric, algebraic, and combinatorial structures. Its study involves interesting combinatorial objects, such as positroids and plabic graphs. Remarkably, the same combinatorial structures appeared in many other areas of mathematics and physics, e.g., in the study of cluster algebras, scattering amplitudes, and solitons. We discuss new ways to think about these structures. In particular, we identify plabic graphs and more general Grassmannian graphs with polyhedral subdivisions induced by 2-dimensional projections of hypersimplices. This implies a close relationship between the positive Grassmannian and the theory of fiber polytopes and the generalized Baues problem. This suggests natural extensions of objects related to the positive Grassmannian.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1142/9789813272880_0177
