Vladimir Fock - Cluster duality and non-holomorphic spectral curves
Автор: Institut des Hautes Etudes Scientifiques (IHES)
Загружено: 2022-11-30
Просмотров: 939
Описание:
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)
Vladimir Fock (Strasbourg University)
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