2021 Fiscal Year Final Research Report
Geometry of discrete groups and its applications
| Project/Area Number |
17K14178
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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 | Kyoto University (2021)
Tohoku University (2017-2020) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Keywords | 離散群 / ランダムウォーク |
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| Outline of Final Research Achievements |
First we introduced a finitely generated group, which we called a discrete affine group, and studied bounded harmonic functions on the group. The result we obtained was published in 2021. Next we studied a comparison problem between harmonic measures and Patterson-Sullivan measures for Gromov hyperbolic groups.
A part of our results was published in 2021. Finally we studied so called product replacement chain and established a cutoff phenomenon for any fixed finite group.
The result was published in 2020.
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| Free Research Field |
離散群論
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| Academic Significance and Societal Importance of the Research Achievements |
指数増大度を持つ従順群の例として離散アファイン群を導入し, その上の有界調和関数の研究を行った成果は、離散群の理解を広げるために行いました. またグロモフ双曲群上のランダムウォークから定まる調和測度とパターソン・サリヴァン測度の比較についての研究は古典的な力学系（カオス的な振る舞いをする測地流など）の研究の自然な発展に位置しています.さらにProduct replacement chainは理論コンピュータ科学において導入され実際に工学的な問題に使われてきました. 我々の成果はこのアルゴリズムの振る舞いの効率性についての知見を与えました.
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