Geometric group theory and metric embedding

2015 Fiscal Year Final Research Report

• Project/Area Number: 23244005
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyoto University (2012-2015); Tohoku University (2011)
• Principal Investigator: Fujiwara Koji 京都大学, 理学(系)研究科(研究院), 教授 (60229078)
• Co-Investigator(Kenkyū-buntansha): OZAWA Narutaka 京都大学, 数理解析研究所, 教授 (60323466) ; SHIOYA Takashi 東北大学, 理学(系)研究科(研究院), 教授 (90235507) ; KAWAZUMI Nariya 東京大学, 数理(科)学研究科(研究院), 准教授 (30214646) ; AKUTAGAWA Kazuo 東北大学, 大学院・情報科学研究科, 教授 (80192920)
• Project Period (FY): 2011-04-01 – 2016-03-31
• Keywords: 幾何学的群論 / 双曲群 / 写像類群 / 作用素環論 / アレクサンドロフ空間 / 擬準同型

Outline of Final Research Achievements

Fujiwara found a new method to embed certain discrete groups into a finite product of hyperbolic graphs in his joint work with Bestvina and Bromberg, and obtained important applications. Ozawa made a significant progress on the study of C*-algebra of discrete amenable groups, and also quasi-homomorphisms into non-commutative groups. Shioya found an important result on the asymptotics of the first eigen value of Laplacians on Alexandrov spaces.

Free Research Field

幾何学