Donaldson-Thomas invariants for the Bridgeland-Smith correspondence

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• Nicholas Williams, University of Cambridge
• Wednesday 16 October 2024, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Dhruv Ranganathan.

Celebrated work of Bridgeland and Smith shows a correspondence between quadratic differentials with prescribed singularities on Riemann surfaces and stability conditions on particular 3-Calabi-Yau triangulated categories. In joint work with Omar Kidwai, we compute the Donaldson-Thomas (DT) invariants appearing for generic stability conditions in these categories. These are enumerative geometric invariants counting the semistable objects. In particular, we show that the value of the DT invariant depends upon the type of finite-length trajectory of the quadratic differential corresponding to the semistable object in the Bridgeland-Smith picture. This verifies predictions for the values of the DT invariants due to Iwaki and Kidwai using the topological recursion of Eynard and Orantin.

This talk is part of the Algebraic Geometry Seminar series.

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