Noncommutative Analysis and Functional Analytic Group Theory

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400114
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: Ozawa Narutaka 京都大学, 数理解析研究所, 教授 (60323466)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 作用素環 / 離散群 / フォンノイマン環 / ランダムウォーク

Outline of Final Research Achievements

Narutaka Ozawa has conducted research on discrete groups under the slogan "Functional analytic group theory." He studied (in collaboration with E. Breuillard, M. Kalantar, and M. Kennedy) the characterization of the simplicity for the reduced group C*-algebra and obtained a breakthrough result. Next, he turned to the harmonic analysis on discrete groups and found a quite simple proof to the famous Gromov theorem stating that a group of polynomial growth is virtually nilpotent. Combining the new method with random walk theory, he (in collaboration with A. Erschler) generalized the Gromov theorem.

Free Research Field

関数解析的群論