POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS
© 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 othe...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
WORLD SCIENTIFIC
2021
|
| Online Access: | https://hdl.handle.net/1721.1/137044 |
| _version_ | 1826193882182844416 |
|---|---|
| author | POSTNIKOV, ALEXANDER |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics POSTNIKOV, ALEXANDER |
| author_sort | POSTNIKOV, ALEXANDER |
| collection | MIT |
| description | © 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. |
| first_indexed | 2024-09-23T09:46:27Z |
| format | Article |
| id | mit-1721.1/137044 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:46:27Z |
| publishDate | 2021 |
| publisher | WORLD SCIENTIFIC |
| record_format | dspace |
| spelling | mit-1721.1/1370442023-04-14T15:44:21Z POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS POSTNIKOV, ALEXANDER Massachusetts Institute of Technology. Department of Mathematics © 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. 2021-11-01T18:50:23Z 2021-11-01T18:50:23Z 2019-05 2021-05-26T11:55:33Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/137044 POSTNIKOV, ALEXANDER. 2019. "POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS." Proceedings of the International Congress of Mathematicians, ICM 2018, 4. en 10.1142/9789813272880_0177 Proceedings of the International Congress of Mathematicians, ICM 2018 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf WORLD SCIENTIFIC arXiv |
| spellingShingle | POSTNIKOV, ALEXANDER POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS |
| title | POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS |
| title_full | POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS |
| title_fullStr | POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS |
| title_full_unstemmed | POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS |
| title_short | POSITIVE GRASSMANNIAN AND POLYHEDRAL SUBDIVISIONS |
| title_sort | positive grassmannian and polyhedral subdivisions |
| url | https://hdl.handle.net/1721.1/137044 |
| work_keys_str_mv | AT postnikovalexander positivegrassmannianandpolyhedralsubdivisions |