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Cluster algebras and the amplituhedron - definition
Multi angle
Authors : Williams, Lauren K. (Author of the conference)
CIRM (Publisher )
05Exx - Algebraic combinatorics
14M15 - Grassmannians, Schubert varieties, flag manifolds
13F60 - Cluster algebras
CIRM (Publisher )
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Abstract :
I will give an introduction to the amplituhedron, a geometric object generalizing the positive Grassmannian, which was introduced by Arkani-Hamed and Trnka in the context of scattering amplitudes in N=4 super Yang Mills theory. I will focus in particular on its connections to cluster algebras, including the cluster adjacency conjecture. (Based on joint works with multiple coauthors, especially Evan-Zohar, Lakrec, Parisi, Sherman-Bennett, and Tessler.)
Keywords : cluster algebras; Grassmannians; amplituhedron
MSC Codes : Keywords : cluster algebras; Grassmannians; amplituhedron
05Exx - Algebraic combinatorics
14M15 - Grassmannians, Schubert varieties, flag manifolds
13F60 - Cluster algebras
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Information on the Video
Film maker : Recanzone, LucaLanguage : English Available date : 20/12/2023 Conference Date : 27/11/2023 Subseries : Research talks arXiv category : Combinatorics Mathematical Area(s) : Algebra ; Combinatorics ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 01:00:46 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-11-27_Williams.mp4 
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Information on the Event
Event Title : Current trends in representation theory, cluster algebras and geometry / Théorie des représentations, algèbres amassées et géométrieEvent Organizers : Amiot, Claire ; Brüstle, Thomas ; Palu, Yann ; Plamondon, Pierre-Guy Dates : 27/11/2023 - 01/12/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2875.html
Citation Data
DOI : 10.24350/CIRM.V.20116303Cite this video as: Williams, Lauren K. (2023). Cluster algebras and the amplituhedron - definition. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20116303 URI : http://dx.doi.org/10.24350/CIRM.V.20116303 |
See Also
- [Multi angle] Khovanov-Seidel braids representation / Author of the conference Queffelec, Hoel.
- [Multi angle] Exact $\infty$-categories / Author of the conference Jasso, Gustavo.
- [Multi angle] Realization spaces of polytopes and oriented matroids / Author of the conference Padrol, Arnau.
- [Multi angle] A$\infty$- categories / Author of the conference Bocklandt, Rafael.
Bibliography
- ARKANI-HAMED, Nima et TRNKA, Jaroslav. The amplituhedron. Journal of High Energy Physics, 2014, vol. 2014, no 10, p. 1-33. - https://arxiv.org/abs/1312.2007
- FOMIN, S., WILLIAMS, L., et ZELEVINSKY, A. Introduction to cluster algebras. chapters 1-3, preprint (2016). arXiv preprint arXiv:1608.05735, 2016. - https://arxiv.org/abs/1608.05735
- PARISI, Matteo, SHERMAN-BENNETT, Melissa, et WILLIAMS, Lauren. The m= 2 amplituhedron and the hypersimplex: signs, clusters, triangulations, Eulerian numbers. arXiv preprint arXiv:2104.08254, 2021. - https://arxiv.org/abs/2104.08254
- WILLIAMS, Lauren K. The positive Grassmannian, the amplituhedron, and cluster algebras. arXiv preprint arXiv:2110.10856, 2021. - https://arxiv.org/abs/2110.10856
- EVEN-ZOHAR, Chaim, LAKREC, Tsviqa, PARISI, Matteo, et al. Cluster algebras and Tilings for the m= 4 amplituhedron. arXiv preprint arXiv:2310.17727, 2023. - https://arxiv.org/abs/2310.17727
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