Short Courses and Seminars 2021

IMSA Seminar

Dr. Daniel Pomerleano
University of Massachusetts

Semi-Affineness of Wrapped Invariants on Affine Log Calabi-Yau Varieties

Friday February 26th, 2021, 4:00pm
Via Zoom
Click here to view video

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). As an application of these finiteness results, we will show that for maximally degenerate log Calabi-Yau varieties equipped with a "homological section," the wrapped Fukaya of X gives an (intrinsic) categorical crepant resolution of the affine variety Spec(SH^0(X)).

This is based on joint work with Sheel Ganatra (https://arxiv.org/abs/1811.03609) and further work in progress.