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Title:
An application of symplectic topology to algebraic geometry
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Abstract:
There is a notion of dimension for triangulated categories which was introduced by Rouquier. Orlov conjectured that the dimension of the bounded derived category of coherent sheaves of a smooth complex variety equals its ordinary Krull dimension. In joint work with Shaoyun Bai, we settled new cases of this conjecture using methods from symplectic geometry, in combination with phonological mirror symmetry. I hope to explain this story and discuss prospects for further work in this direction.
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