Intrinsic mirror symmetry and categorical crepant resolutions

Gross and Siebert have recently proposed an "intrinsic" programme for studying mirror symmetry. In this talk, we will discuss a symplectic interpretation of some of their ideas in the setting of affine log Calabi-Yau varieties. Namely, we describe work in progress which shows that, under suitable assumptions, the wrapped Fukaya category of such a variety XX gives an intrinsic "categorical crepant resolution" of Spec(SH0(X))Spec(SH0(X)). No background in mirror symmetry will be assumed for the talk.