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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Cluster Algebra Via Non-Archimedean Enumerative Geometry

## Cluster Algebra Via Non-Archimedean Enumerative GeometryAdd to your list(s) Download to your calendar using vCal - Tony Yue Yu (Université Paris Saclay)
- Tuesday 09 November 2021, 15:30-16:15
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. CARW03 - Interdisciplinary applications of cluster algebras I will discuss the mirror symmetry of cluster varieties via the enumeration of non-archimedean analytic curves. We construct a canonical scattering diagram by counting infinitesimal non-archimedean cylinders bypassing the Kontsevich-Soibelman algorithm. We prove adic convergence, ring homomorphism, finite polyhedral approximation, theta function consistency and Kontsevich-Soibelman consistency. Furthermore, we prove a comparison theorem with the combinatorial constructions of Gross-Hacking-Keel-Kontsevich. This has two-fold implications: First it gives a concrete combinatorial way for computing the abstract non-archimedean curve counting in the case of cluster varieties; conversely, we obtain geometric interpretations of various combinatorial constructions and answer several conjectures of GHKK . Joint work with S. Keel. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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