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 gen- eralization of duality between integers and the multiplicative group.) In the talk we will suggest related geometric interpretations of the tropical points of the A- variety for local system of the curve. On on 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 a measured laminaiton. On the other hand it can be interpreted as a class 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 local system on the curve with values in the affine group. (Joint with A.Thomas and V.Tatitscheff)
By Paul-André Melliès
By Paul-André Melliès
By Cyril Banderier
By Sergey Yurkevich
By Karol Penson
By Frédéric Patras
By Darij Grinberg
By Travis Scrimshaw
By Arthemy Kiselev
By Béa de Laporte
By Viviane Pons
By Gérard Ben Arous
By Viviane Pons
By Wenjie Fang
By Misha Gromov
By Céline Duval
By Olivier Benoist
