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Mark Gross: Lectures

January 7, 2019 and January 8, 2019

ABSTRACT: Starting from the Strominger-Yau-Zaslow conjecture of 1996, I will attempt to explain how the differential geometric ideas of that
conjecture evolved into the current algebro-geometric and tropical viewpoint of mirror symmetry espoused by myself and Siebert.

January 10, 2017
TITLE: Gromov-Hausdorff collapse for abelian fibred Calabi-Yau varieties

ABSTRACT: I will describe joint work with Tosatti and Zhang on collapsing of sequences of Ricci-flat metrics on Calabi-Yau manifolds with abelian variety fibrations where the volume of the fibres goes to zero. In particular, if the base of the fibration is of dimension one, we show the limit metric space is homeomorphic to the base. In particular, this extends an old result of myself and Wilson for elliptically fibred K3 surfaces to allow any kind of singular fibre.