Séminaire de Géométrie Tropicale

Institut Mathématiques de Jussieu ,
Université Pierre et Marie Curie, Paris 6
UMR CNRS 7586



23 Mai 2012, 16h15 salle 1525-5-02



Yan Soibelman (Kansas State University)

Résumé : Integrable systems, tropical geometry and Donaldson-Thomas invariants

I am going to discuss three conjecturally equivalent ways to describe DT-invariants of local Calabi-Yau 3-folds:

a) geometric one,based on the count of special Lagrangian submanifolds;

b) tropical one, based on the count of tropical trees on the base of the corresponding Hitchin integrable system;

c) algebro-geometric one,based on the deformation theory of the wheel of projective lines in a toric variety.

There are many interesting connections between a),b),c) as well as their relationship to the count of geodesics of quadratic differentials, representations of quivers and cluster algebras.