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Dynamics and DT invariants

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EMGW05 - Moduli stacks and enumerative geometry

An intensely studied problem in dynamical systems is to count the saddle connections and closed cylinders of a quadratic differential on a Riemann surface. I will explain how this problem can be seen as a particular example of the general problem of counting stable objects in 3-d Calabi—Yau categories using Donaldson-Thomas theory a la Kontsevich-Soibleman. As a consequence, these counts satisfy the wall-crossing formula which relates the DT invariants at different points in the space of stability conditions. The relevant 3CY category is a Fukaya-type category and conjecturally mirror to a certain category of coherent sheaves on an open 3CY variety. Based on arXiv:2104.06018.

This talk is part of the Isaac Newton Institute Seminar Series series.

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