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Quantum cohomology for isotropic Grassmannians and Lefschetz exceptional collections

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Quantum cohomology for isotropic Grassmannians and Lefschetz exceptional collections
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18
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We will show by "generic smoothness" that the big quantum cohomology ring of isotropic Grassmannians IG(2,2n) is generically semisimple but the small quantum cohomology ring is not. That non-semisimplicity leads to a decomposition of the small quantum cohomology ring that relates to a certain decomposition of the derived category of IG(2,2n) in a so-called Lefschetz exceptional collection. This is based on joint work with A. Mellit, A. Kuznetsov, N. Perrin and M. Smirnov.