Noncommutative Analysis and Functional Analytic Group Theory
| Project/Area Number |
26400114
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
Ozawa Narutaka 京都大学, 数理解析研究所, 教授 (60323466)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 作用素環 / 離散群 / フォンノイマン環 / ランダムウォーク / 解析的群論 / 作用素環論 / 因子環 / C*環 / von Neumann環 |
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| 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.
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Report
(4 results)
Research Products
(25 results)
