## 談話会・数理科学講演会

担当者 加藤晃史、北山貴裕、辻雄（委員長）、三竹大寿 https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index.html

### 2014年01月24日(金)

16:30-17:30   数理科学研究科棟(駒場) 002号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

Bo Berndtsson 氏 (Chalmers University of Technology)
Complex Brunn-Minkowski theory (ENGLISH)
[ 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.