Starts 4 Feb 2015 14:30
Ends 4 Feb 2015 15:30
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Stability conditions and Frobenius manifolds
ICTP
Leonardo Building - Luigi Stasi Seminar Room
Abstract:
These talks will be about spaces of stability conditions on Calabi-Yau quiver algebras. I want to discuss some not-very-well understood connections with the theory of semi-simple Frobenius manifolds. I will start with the usual motivation for stability conditions coming from mirror symmetry, before discussing the example of the A_n quiver where one can make a precise connection with the Frobenius-Saito structure on the unfolding space of the corresponding simple singularity. I will then consider the case of stability conditions on (local) P^2, which should be closely related to the quantum cohomology of P^2, although so far this link is mostly conjectural. Finally, I will discuss the Kontsevich-Soibelman wall-crossing formula, which is the natural geometric structure existing on spaces of stability conditions in the Calabi-Yau threefold setting.
These talks will be about spaces of stability conditions on Calabi-Yau quiver algebras. I want to discuss some not-very-well understood connections with the theory of semi-simple Frobenius manifolds. I will start with the usual motivation for stability conditions coming from mirror symmetry, before discussing the example of the A_n quiver where one can make a precise connection with the Frobenius-Saito structure on the unfolding space of the corresponding simple singularity. I will then consider the case of stability conditions on (local) P^2, which should be closely related to the quantum cohomology of P^2, although so far this link is mostly conjectural. Finally, I will discuss the Kontsevich-Soibelman wall-crossing formula, which is the natural geometric structure existing on spaces of stability conditions in the Calabi-Yau threefold setting.