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About the categorical strong rationality conjecture for flopping curves

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

The strong rationality conjecture of Pandharipande—Thomas is the PT version of the Gopakumar—Vafa formula for Gromov—Witten invariants. This has been reformulated by Toda as the independence of the count of one dimensional sheaves from their Euler characteristic. I will try to motivate why, in order to prove this independence, it might be convenient to work with cohomological Donaldson—Thomas invariants. In the last part of the talk I will concentrate on the case of flopping curves, state the cohomological version of the conjecture, and give an outline of the (almost completed) proof we give. This is based on a joint work in progress with S. Beentjes and B. Davison.

This talk is part of the Algebraic Geometry Seminar series.

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