| Project/Area Number |
26800029
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 離散群 / グラフ / 調和関数 / 調和測度 / 双曲群 / 従順群 / 離散群論 / Poisson境界 / 語双曲群 / Liouville性 / ランダムウォーク / Gromov双曲群 / ランダムDirichlet級数 |
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| Outline of Final Research Achievements |
It is expected to develop geometry on discrete objects in connections not only to mathematics but also to other fields in natural sciences. Our research focuses on problems in mathematics and related fields, in particular analysis on discrete groups and graphs, as they form an active research area in recent years. The topic is also related to mathematical aspects of computer sciences and statistical physics. In order to deepen our understanding on discrete groups, we introduced a new class of groups, and have studied its basic property.
This clarified its relations to other well-studied groups which had been difficult to analyze.
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