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Sébastien Boucksom: Lectures

January 8, 2019 and January 9, 2019
TITLE: The essential skeleton of a Calabi-Yau degeneration

ABSTRACT: To any meromorphic degeneration of complex projective varieties corresponds a projective variety over the field of Laurent series, and hence a non-Archimedean analytic space in the sense of Berkovich. This applies in particular to a degeneration of polarized Calabi-Yau manifolds, and has been used in recent years by Nicaise, Xu and their collaborators to approach a version of the Ströminger-Yau-Zaslow conjecture due to Kontsevich-Soibelman. I will provide a gentle introduction to this circle of ideas, mostly based on a joint work with Jonsson, in which the limit of Calabi-Yau volume forms in the associated Berkovich space is analyzed.