数理談話会

日時: 2014年01月24日(金) 16:30〜17:30
会場: 東京大学 大学院数理科学研究科 002号室

講演者

Bo Berndtsson 氏 (Chalmers University of Technology)

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講演題目

Complex Brunn-Minkowski theory

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講演概要

The classical Brunn-Minkowski theory deals with the volume of convex sets. It can be formulated as a statement about how the volume of slices of a convex set varies when the slice changes. Its complex counterpart deals with slices of pseudo convex sets, or more generally fibers of a complex fibration. It describes how $L^2$-norms of holomorphic functions, or sections of a line bundle, vary when the fibers change, and says essentially that a certain associated vector bundle has positive curvature. In the presence of enough symmetry this implies convexity properties of volumes; the real Brunn-Minkowski theorem corresponding to maximal symmetry. There are also applications and relations in other directions, like variations of Kahler metrics, variations of complex structures and the study of plurisubharmonic functions.