Mirror Symmetry for Rank 2 Cluster Varieties
Duration: 37 mins 55 secs
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About this item
| Description: |
Dr Man Wai Cheung (Harvard University)
9th November 2021 | 13:45 - 14:15 |
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| Created: | 2021-11-10 10:39 |
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| Collection: | Cluster algebras and representation theory |
| Publisher: | Isaac Newton Institute for Mathematical Sciences |
| Copyright: | Dr Man Wai Cheung |
| Language: | eng (English) |
| Abstract: | The Gross-Hacking-Keel mirror is constructed in terms of scattering diagrams and theta functions. The ground of the construction is that scattering diagrams inherit the algebro-geometric analogue of the holomorphic disks counting. With Sam Bardwell-Evans, Hansol Hong, and Yu-shen LIn, we construct a special Lagrangian fibration on the non-toric blowups of toric surfaces that contains nodal fibres, and prove that the fibres bounding Maslov 0 discs reproduce the scattering diagrams. As a consequence, we can then illustrate the mirror duality between the A and X cluster varieties. |
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