Cluster Algebra Via Non-Archimedean Enumerative Geometry
Duration: 44 mins 32 secs
Share this media item:
Embed this media item:
Embed this media item:
About this item
| Description: |
Professor Tony Yue Yu (Université Paris Saclay)
9th November 2021 | 15:30 - 16:15 |
|---|
| Created: | 2021-11-10 10:42 |
|---|---|
| Collection: | Cluster algebras and representation theory |
| Publisher: | Isaac Newton Institute for Mathematical Sciences |
| Copyright: | Professor Tony Yue Yu |
| Language: | eng (English) |
| Abstract: | 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. |
|---|---|
Available Formats
| Format | Quality | Bitrate | Size | |||
|---|---|---|---|---|---|---|
| MPEG-4 Video | 1080x720 | 2.73 Mbits/sec | 913.58 MB | View | Download | |
| MPEG-4 Video | 540x360 | 861.57 kbits/sec | 281.02 MB | View | Download | |
| WebM | 1080x720 | 1.42 Mbits/sec | 477.69 MB | View | Download | |
| WebM | 540x360 | 356.88 kbits/sec | 116.45 MB | View | Download | |
| iPod Video | 480x270 | 482.33 kbits/sec | 157.32 MB | View | Download | |
| MP3 | 44100 Hz | 249.74 kbits/sec | 81.55 MB | Listen | Download | |
| Auto * | (Allows browser to choose a format it supports) | |||||