Intrinsic Mirror Symmetry and Categorical Crepant Resolutions

Abstract: A general expectation in mirror symmetry is that the mirror partner to an affine log Calabi-Yau variety is "semi-affine" (meaning it is proper over its affinization). We will discuss how the semi-affineness of the mirror can be seen directly as certain finiteness properties of Floer theoretic invariants of X (the symplectic cohomology and wrapped Fukaya category). One interesting consequence of these finiteness results is that, under fairly general circumstances, the wrapped Fukaya of X gives an ("intrinsic") categorical crepant resolution of the affine variety Spec(SH^0(X)). This is based on arxiv.org/pdf/2103.01200.pdf.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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