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| Name | Andy Hone — New cluster algebras from old: deformations of finite type |
| Video Uploader | Video From Mathematical Physics School |
| Upload Date | This Video Uploaded At 13-07-2024 07:53:15 |
| Video Discription | The periodic Y -systems discovered by Zamolodchikov in the context of perturbed conformal field theories provided one of the original motivations for Fomin & Zelevinsky's theory of cluster algebras. One of the first main results in the theory was the classification of finite type cluster algebras, whose seeds were shown to be in one-to-one correspondence with the finite Dynkin types (up to mutation equivalence). Here we describe how deformations of the finite type case produce discrete dynamical systems that, while no longer completely periodic, are completely integrable in the Liouville sense. By lifting the dynamics to higher dimensional maps with the Laurent property (“Laurentification”) we find new families of cluster algebras with mutation periodicity. This is based on joint work we began with Kouloukas, and have continued with Grabowski, Kim and Mase. |
| Category | Entertainment |
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