Introduction to cluster algebras and varieties. 2022

Zoom meeting 880 0460 1519, password: "number of roots in A_4" -- number, 2 digits

Plan of the course.
  1. Prelimiary examples Notes (updated 04.12.2022).
  2. Seeds. Mutations. Laurent phenomenon Notes (updated 04.12.2022).
  3. Total positivity. Notes (updated 13.12.2022).
  4. Double Bruhat cells. X coordinates Notes (updated 26.12.2022).
  5. Cluster Poisson structure. Poisson Lie groups Notes (updated 26.12.2022).
  6. Cluster Poisson structure. Integrable systems Notes (updated 26.12.2022).
  7. Upper cluster algebra. Coordinate rings on double Bruhat cells Notes (updated 04.12.2022).
  8. Starfish Lemma. Grassmanians Notes (updated 13.12.2022).
  9. Plabic graphs. Grassmanians. Notes (updated 22.12.2022).
  10. Poisson structures on Grassmanians. Notes (updated 22.12.2022).
  11. Geometric approach to cluster varieties. Notes (updated 26.12.2022).
  12. Cluster structure on the space of framed local systems. PGL_2 case Notes (updated 28.12.2022).
  13. Pinnings Notes (updated 28.12.2022).
  14. Cluster structure on the space of framed local systems. PGL_m case Notes (updated 28.12.2022).

Problems (updated 26.12.2022).

Recordings of the lectures playlist.