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Discrete mathematical modelling seminar
Seminar information archive ～04/26｜Next seminar｜Future seminars 04/27～
| Organizer(s) | Tetsuji Tokihiro, Ralph Willox |
|---|
2023/06/08
18:15-19:15 Online
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Andy Hone (University of Kent)
Deformations of Zamolodchikov periodicity, discrete integrability and the Laurent property (English)
This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.
Andy Hone (University of Kent)
Deformations of Zamolodchikov periodicity, discrete integrability and the Laurent property (English)
[ Abstract ]
Zamolodchikov periodicity was a conjectured property of Y-systems observed in exactly solvable models of quantum field theory associated with simple Lie algebras. The advent of Fomin & Zelevinsky's theory of cluster algebras provided an ideal mathematical framework for proving and formulating extensions of this property. Recently we have found a family of birational maps which deforms the periodic dynamics observed by Zamolodchikov, and destroys the Laurent property that is an inherent feature of cluster dynamics, but still preserves integrability. In this talk we present a variety of examples of deformed integrable maps in types A, B & D, and show how to restore the Laurent property in higher dimensions. This is the combined result of joint work with Grabowski, Kouloukas, Kim and Mase.
Zamolodchikov periodicity was a conjectured property of Y-systems observed in exactly solvable models of quantum field theory associated with simple Lie algebras. The advent of Fomin & Zelevinsky's theory of cluster algebras provided an ideal mathematical framework for proving and formulating extensions of this property. Recently we have found a family of birational maps which deforms the periodic dynamics observed by Zamolodchikov, and destroys the Laurent property that is an inherent feature of cluster dynamics, but still preserves integrability. In this talk we present a variety of examples of deformed integrable maps in types A, B & D, and show how to restore the Laurent property in higher dimensions. This is the combined result of joint work with Grabowski, Kouloukas, Kim and Mase.
