Cluster integrable systems. Advanced topics
1. Reminder: cluster varieties, Poisson-Lie groups and integrable systems.
2. The Goncharov-Kenyon construction, bipartite graphs and dimers.
3. Faces, zigzag paths and Newton polygons. Poisson and dual quivers.
4. Dimer partition function, faces and loops, dual surface and spectral curve.
5. Integrability: Liouville-Arnold theorem from Pick's formula.
6. Examples of the Goncharov-Kenyon systems, back to Toda chains.
7. Isomorphisms, SL(A,Z) transformations and polygon mutations.
8. Decorated Newton polygons and cluster reductions. Examples.
9. Deautonomization of cluster integrable systems and supersymmetric gauge theories.
2. The Goncharov-Kenyon construction, bipartite graphs and dimers.
3. Faces, zigzag paths and Newton polygons. Poisson and dual quivers.
4. Dimer partition function, faces and loops, dual surface and spectral curve.
5. Integrability: Liouville-Arnold theorem from Pick's formula.
6. Examples of the Goncharov-Kenyon systems, back to Toda chains.
7. Isomorphisms, SL(A,Z) transformations and polygon mutations.
8. Decorated Newton polygons and cluster reductions. Examples.
9. Deautonomization of cluster integrable systems and supersymmetric gauge theories.
讲师
Andrei Marshakov
日期
2025年11月05日 至 12月31日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三 | 13:30 - 16:05 | Shuangqing | Zoom 15 | 204 323 0165 | BIMSA |
听众
Graduate
视频公开
公开
笔记公开
公开
语言
英文