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.
Lecturer
Andrei Marshakov
Date
5th November ~ 31st December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 13:30 - 16:05 | Shuangqing | Zoom 15 | 204 323 0165 | BIMSA |
Audience
Graduate
Video Public
Yes
Notes Public
Yes
Language
English