研究者データベース

尾國 新一オグニ シンイチ

所属部署名大学院理工学研究科 数理物質科学専攻
職名准教授
Last Updated :2019/11/12

研究者基本情報

基本情報

氏名

  • 氏名

    尾國 新一
  • 氏名(カナ)

    オグニ シンイチ

学歴等

学位

  • 博士(理学)

研究活動情報

著書・発表論文等

論文

講演・口頭発表等

MISC

  • Coarse compactifications and controlled products, Tomohiro Fukaya, Shin-ichi Oguni, Takamitsu Yamauchi, 2018年10月, http://arxiv.org/abs/1810.08720v1, We introduce the notion of controlled products on metric spaces as a generalization of Gromov products, and construct boundaries by using controlled products, which we call the Gromov boundaries. It is shown that the Gromov boundary with respect to a controlled product on a proper metric space complements the space as a coarse compactification. It is also shown that there is a bijective correspondence between the set of all coarse equivalence classes of controlled products and the set of all equivalence classes of coarse compactifications.
  • Blowing up and down compacta with geometrically finite convergence actions of a group, Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata, 2012年01月, http://arxiv.org/abs/1201.6104v3, 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, http://arxiv.org/abs/1109.2663v3, 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.
  • L2-invariants of groups under coarse equivalence and of groupoids under Morita equivalence, Shin-ichi Oguni, preprint, 2010年08月, We prove that triviality of some L2-invariants of discrete groups is preserved by coarse equivalence, where L2-invariants are L2-homologies, L2-Betti numbers (with `a mild condition') and Novikov-Shubin invariants. We give definitions of some L2-invariants of cocompact etale groupoids and prove that their triviality is preserved by Morita equivalence. Also we exhibit basic properties for modules over von Neumann algebras which are not necessarily finite. This paper contains an appendix by Yamashita, where a characterization of finite von Neumann algebras is given.

その他研究情報

競争的資金

愛媛大学教員活動実績

教育活動(B)

担当授業科目(B01)

  • 2019年, 前期, 学部, 線形代数Ⅰ
  • 2019年, 前期, 学部, 卒業研究Ⅰ
  • 2019年, 前期, 学部, 解析学Ⅰ
  • 2019年, 前期, 学部, 幾何学Ⅰ
  • 2019年, 前期, 修士, 数理科学ゼミナールⅠ


Copyright © MEDIA FUSION Co.,Ltd. All rights reserved.