Nov 28 – 29, 2022
Le Bois-Marie
Europe/Paris timezone

Cluster Duality and Non-holomorphic Spectral Curves

Nov 29, 2022, 5:45 PM
Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Centre de conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette


Prof. Vladimir FOCK (Strasbourg University)


Cluster duality is a correspondence between tropical points of a cluster A-variety and a canonical basis of functions on the corresponding X-variety. (It is a generalization of duality between integers and the multiplicative group.) In the talk, we will suggest related geometric interpretations of the tropical points of the Avariety for a local system of the curve. On the hand, it can be considered as a class of graphs on the surfaces colored by generators of the affine Weyl group. This is a generalization of the notion of measured lamination. On the other hand, it can be interpreted as a class of Lagrangian coverings in the cotangent bundle to the curve representing integer classes of homology. Finally, they are related to the ”cells” of the space of the local system on the curve with values in the affine group.
Joint with A.Thomas and V.Tatitscheff.

Presentation materials

There are no materials yet.