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尾國 新一オグニ シンイチ

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大学院理工学研究科 数理物質科学専攻
職名准教授
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Last Updated :2018/02/08

研究者基本情報

学位

  • 博士(理学)

研究活動情報

論文

MISC

  • A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture
    Tomohiro Fukaya, Shin-ichi Oguni,   2017年05月16日, We establish a coarse version of the Cartan-Hadamard theorem, which states that proper coarsely convex spaces are coarsely homotopy equivalent to the open cones of their ideal boundaries. As an application, we show that such spaces satisfy the coarse Baum-Connes conjecture. Combined with the result of Osajda-Przytycki, it implies that systolic groups and locally finite systolic complexes satisfy the coarse Baum-Connes conjecture.
  • On coarse geometric aspects of the Hilbert geometry
    Ryosuke Mineyama, Shin-ichi Oguni,   2014年12月, We give a necessary and sufficient condition for the natural boundary of a Hilbert geometry to be a corona. In addition, we show that any Hilbert geometry is uniformly contractible and with bounded coarse geometry. As a consequence of these we see that the coarse Novikov conjecture holds for a Hilbert geometry under a mild condition. Also we show that the asymptotic dimension of any two-dimensional Hilbert geometry is just two.
  • Blowing up and down compacta with geometrically finite convergence actions of a group
    Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata,   2012年01月, We consider two compacta with minimal non-elementary convergence actions of a countable group. When there exists an equivariant continuous map from one to the other, we call the first a blow-up of the second and the second a blow-down of the first. When both actions are geometrically finite, it is shown that one is a blow-up of the other if and only if each parabolic subgroup with respect to the first is parabolic with respect to the second. As an application, for each compactum with a geometrically finite convergence action, we construct its blow-downs with convergence actions which are not geometrically finite.
  • Hyperbolically embedded virtually free subgroups of relatively hyperbolic groups
    Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata,   2011年09月, We show that if a group is not virtually cyclic and is hyperbolic relative to a family of proper subgroups, then it has a hyperbolically embedded subgroup which contains a finitely generated non-abelian free group as a finite index subgroup.

講演・口頭発表等

  • 粗幾何版アダマール・カルタンの定理とその応用
    尾國 新一, 松山TGSAセミナー,   2017年10月
  • On coarse homotopy
    Shin-ichi Oguni, 集合論的・幾何学的トポロジーの動向と諸分野との連携,   2017年06月
  • 粗ホモトピーについて
    尾國新一, 第3回幾何学的群論若手勉強会,   2017年03月
  • Hilbert幾何の粗幾何的性質
    白浜研究集会,   2016年03月
  • Osajdaによるエクスパンダーを含む群とその周辺
    尾國新一, 春の代数的位相幾何学セミナー~幾何的アプローチ,   2016年03月
  • Coronae of product spaces and the coarse Baum-Connes conjecture
    Shin-ichi Oguni, Conference on Non-commutative Geometry and K-Theory,   2015年12月
  • 粗Baum-Connes予想と粗幾何
    尾國新一, 広島幾何学研究集会2015,   2015年10月
  • 非有界距離空間の大尺度幾何と無限遠
    尾國 新一, 松山TGSAセミナー,   2015年06月
  • 粗Baum-Connes予想と粗代数的トポロジー
    尾國新一, 日本数学会2014年度秋季総合分科会,   2014年09月, 招待有り
  • Coarse Baum-Connes conjecture and coarse algebraic topology
    Shin-ichi Oguni, Rigidity School, Tokyo 2013/2014,   2014年01月
  • Coronae and coarse homologies
    Shin-ichi Oguni, Metric geometry and analysis,   2013年12月
  • An introduction to the coarse Baum-Connes conjecture
    尾國新一, 非可換幾何 湯谷研究集会,   2013年11月
  • On the coarse Baum-Connes conjecture
    Shin-ichi Oguni, GEOQUANT 2013,   2013年08月

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