Researcher Database

Toshiyuki Akita
Faculty of Science Mathematics Mathematics
Professor

Researcher Profile and Settings

Affiliation

  • Faculty of Science Mathematics Mathematics

Job Title

  • Professor

J-Global ID

Research Interests

  • group cohomology   topology   quandle   discrete group   Coxeter group   Euler characteristic   characteristic class   mapping class group   classifying space   Artin group   homotopy theory   algebraic topology   Remann surface   

Research Areas

  • Natural sciences / Geometry

Academic & Professional Experience

  • 2017/04 - Today Hokkaido University Faculty of Science
  • 2007/04 - 2017/03 Hokkaido University Faculty of Science
  • 2006/04 - 2007/03 Hokkaido University Faculty of Science
  • 1999/08 - 2006/03 Hokkaido University
  • 1995/04 - 1999/07 Fukuoka University Faculty of Science
  • 1994/04 - 1995/03 日本学術振興会 特別研究員(DC3)

Association Memberships

  • 日本数学会   

Research Activities

Published Papers

  • Toshiyuki Akita, Ye Liu
    Algebraic and Geometric Topology 18 (1) 547 - 568 1472-2739 2018/01/10 [Refereed][Not invited]
     
    In this paper, we compute the second mod 2 homology of an arbitrary Artin group, without assuming the K(π, 1) conjecture. The key ingredients are (A) Hopf’s formula for the second integral homology of a group and (B) Howlett’s result on the second integral homology of Coxeter groups.
  • Toshiyuki Akita, Ye Liu
    JOURNAL OF ALGEBRA 473 132 - 141 0021-8693 2017/03 [Refereed][Not invited]
     
    We obtain vanishing ranges for the mod p cohomology of alternating subgroups of finite p-free Coxeter groups. Here a Coxeter group W is p-free if the order of the product st is prime to p for every pair of Coxeter generators s, t of W. Our result generalizes those for alternating groups formerly proved by Kleshchev-Nakano and Burichenko. As a byproduct, we obtain vanishing ranges for the twisted cohomology of finite p-free Coxeter groups with coefficients in the sign representations. In addition, a weak version of the main result is proved for a certain class of infinite Coxeter groups. (C) 2016 Elsevier Inc. All rights reserved.
  • Toshiyuki Akita
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 48 (6) 945 - 956 0024-6093 2016/12 [Refereed][Not invited]
     
    Given an odd prime number p and a Coxeter group W such that the order of the product st is prime to p for all Coxeter generators s, t of W, we prove that the p-local homology groups H-k(W, Z((p))) vanish for 1 <= k <= 2(p - 2). This generalizes a known vanishing result for symmetric groups due to Minoru Nakaoka.
  • Toshiyuki Akita
    PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES 47 (4) 897 - 909 0034-5318 2011/12 [Refereed][Not invited]
     
    We prove periodicity for mod p Mumford-Morita-Miller classes of surface symmetries and thereby for finite subgroups of mapping class groups. As an application, we obtain a couple of vanishing results for mod p Mumford-Morita-Miller classes for surface symmetries.
  • Toshiyuki Akita, Nariya Kawazumi
    MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY 144 (2) 411 - 421 0305-0041 2008/03 [Refereed][Not invited]
     
    The first author conjectured certain relations for Morita-Mumford classes and Newton classes in the integral cohomology of mapping class groups (integral Riemann-Roch formulae). In this paper, the conjecture is verified for cyclic subgroups of mapping class groups.
  • Toshiyuki Akita
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 136 (7) 2571 - 2573 0002-9939 2008 [Refereed][Not invited]
     
    An alternative formula for the Euler characteristics of even dimensional triangulated manifolds is deduced from the generalized Dehn-Sommerville equations.
  • On mod p Riemann-Roch formulae for mapping class groups
    Toshiyuki Akita
    Adv. Stud. Pure Math. 52 111 - 118 2008 [Refereed][Invited]
  • The adjoint group of a Coxeter quandle
    Toshiyuki Akita
    The adjoint group of a Coxeter quandle (to appear) [Refereed][Not invited]

Conference Activities & Talks

  • Artin群とCoxeterカンドルの随伴群のコホモロジー  [Invited]
    秋田利之
    森本雅治先生退職記念研究集会  2020/02
  • Toshiyuki Akita
    The Third Pan Pacific International Conference on Topology and Applications (PPICTA)  2019/11  成都(中国)
  • Toshiyuki Akita
    Branched Coverings, Degenerations, and Related Topics 2019  2019/03  広島大学(東広島キャンパス)大学院理学研究科
  • 秋田利之
    九州大学トポロジー金曜セミナー  2018/12
  • 秋田利之
    九州大学数理談話会  2018/12
  • 秋田利之
    2018年度ホモトピー論シンポジウム  2018/11
  • 秋田利之
    ホモトピー沖縄  2018/09
  • 秋田利之
    Matroids, reflection groups, and free hyperplane arrangements  2018/06  RIMS
  • Coxeter groups, Artin groups and Coxeter quandles  [Invited]
    Toshiyuki Akita
    研究集会「ストリングトポロジーとその周辺」  2017/12  四季の湯強羅静雲荘
  • カンドルと対称群の中心拡大  [Invited]
    秋田利之
    北海道大学数学教室談話会  2017/10
  • On the mod p cohomology of Coxeter groups and their alternating subgroups  [Not invited]
    Toshiyuki Akita
    ホモトピー論シンポジウム  2016/11  県立広島大学サテライトキャンパス
  • Second mod 2 homology of Artin groups  [Invited]
    Toshiyuki Akita
    東大火曜トポロジーセミナー  2016/11
  • Cohomology of Coxeter groups and related groups  [Invited]
    Toshiyuki Akita
    Perspectives on arrangements and configuration spaces  2016/09  Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore di Pisa
  • Crossed modules and Artin groups  [Invited]
    Toshiyuki Akita
    京大代数トポロジーセミナー  2016/06

MISC

Educational Activities

Teaching Experience

  • Geometry B
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : チェイン複体,ホモロジー群,完全系列
  • Linear Algebra I
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 行列, 連立1次方程式, 基本変形, 階数, 行列式, 逆行列
  • Introductory Linear Algebra
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 連立1次方程式, 逆行列, 固有値, 固有ベクトル
  • Exercises on Geometry
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 多様体,ホモロジー

Campus Position History

  • 2017年10月26日 
    2019年3月31日 
    経営戦略室室員
  • 2017年4月1日 
    2019年3月31日 
    総長補佐
  • 2017年4月1日 
    Present 
    評価室室員
  • 2019年4月1日 
    Present 
    経営戦略室室員
  • 2019年4月1日 
    Present 
    総長補佐

Position History

  • 2017年10月26日 
    2019年3月31日 
    経営戦略室室員
  • 2017年4月1日 
    2019年3月31日 
    総長補佐
  • 2017年4月1日 
    Present 
    評価室室員
  • 2019年4月1日 
    Present 
    経営戦略室室員
  • 2019年4月1日 
    Present 
    総長補佐


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