Publications and Talks

Papers

Preprints

[17] Blown-up corona of relatively hyperbolic groups, arXiv:2402.11501
[16] Boundary of free products of metric spaces, (with T.Matsuka) arXiv:2402.06862

Publications

[15] Free products of coarsely convex spaces and the coarse Baum-Connes conjecture, (with T.Matsuka) arXiv:2303.13701, to appear in Kyoto J.Math.
[14] A topological decomposition of Busemann space J. Math. Soc. Japan 76(1): 269-281 (January, 2024). DOI: 10.2969/jmsj/89738973
[13] Visual maps between coarsely convex spaces (with Y.Ezawa) Kobe J. Math. 40 no. 7 - 45 (2023)
[12] Coarse compactifications and controlled products (with S.Oguni and T.Yamauchi), Journal of Topology and Analysis, Vol. 14, No. 04, pp. 875-900 (2022)
[11] A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture (with S.Oguni), Journal of Topology and Analysis, Vol. 12, No. 03, pp. 857-895 (2020), DOI:10.1142/S1793525319500675
[10] Coronae of relatively hyperbolic groups and coarse cohomologies (with S.Oguni), Journal of Topology and Analysis,1 September 2015, DOI: 10.1142/S1793525316500151
[9] Coronae of product spaces and the Coarse Baum-Connes conjecture (with S.Oguni), Advances in Mathematics, volume 279, 16 July 2015, Pages 201–233
[8] The coarse Baum-Connes conjecture for Busemann non-positively curved spaces (with S.Oguni), Kyoto Journal of Mathematics, vol. 56, issue 1 (2016)
[7] Growth of Critical Points in One-Dimensional Lattice Systems (with M.ASAOKA, K.MITSUI, M.TSUKAMOTO), Journal d'Analyse Mathematique, vol. 127, issue 1 (2015)
[6] Coarse Baum-Connes conjecture for relatively hyperbolic groups (with S.Oguni), Journal of Topology and Analysis, Vol. 4, Issue 1 (2012), 99-113.
[5] Sublinear Higson corona of Euclidean cone, Tsukuba Journal of Mathematics, Vol. 36, Number 1 (2012), 67-77.
[4] Remark on dynamical Morse inequality (with M.Asaoka and M.Tsukamoto), Proc. Japan Acad. Ser. A Math. Sci. Vol. 87, No. 9 (2011), 178-182.
[3] Coarse dynamics and fixed point property, Nagoya Mathematical Journal. Vol. 202 (2011), 1-13 DOI 10.1215/00277630-1260414
[2] Asymptotic distribution of critical values, (with M.Tsukamoto), Geometriae Dedicata Vol. 143, No. 1(2009)
[1] Application of Gr\"{o}bner Bases to the Cup-Length of Oriented Grassmann Manifolds, Homology, Homotopy and Applications, Vol. 10 (2008), No. 2, pp.195-209. DOI:10.4310/HHA.2008.v10.n2.a10

Book

粗幾何学入門, サイエンス社 SGCライブラリ 152

Talks

  1. Visual maps between coarsely convex spaces
    福岡大学微分幾何研究集会, 福岡大学　2023年11月3日
  2. Busemann空間の位相的分解
    1. 日本数学会秋季総合分科会・幾何学分科会, 北海道大学 2022年9月15日
    2. 大阪大学幾何学セミナー, 大阪大学 2022年10月24日
  3. Visual maps between coarsely convex spaces
    1. Geometric Group Theory in East Asia (online seminar) , May 28 2021
    2. 集合論的および幾何学的トポロジーと関連分野への応用, June 6
  4. 粗凸空間に作用する群の例
    1. 日本数学会秋季総合分科会・幾何学分科会, 金沢大学 2019年9月19日
    2. リーマン幾何学，粗幾何学，特異点, 横浜国立大学 2019年11月8日
  5. 粗幾何学入門1,2
    阿蘇幾何学研究集会 2019年9月1日, 2日
  6. Coarsely convex spaces
    1. Rigidity School ― The Final Meeting　名古屋大学　2018年9月17日
    2. AMS Spring Central and Western Joint Sectional Meeting，Special Session on Coarse Geometry, Index Theory, and Operator Algebras: Around the Mathematics of John Roe March 24, 2019
  7. 粗凸空間と粗 Cartan−Hadamard の定理
    1.福岡大学微分幾何セミナー，2018年11月15日
    2.リーマン幾何と幾何解析，筑波大学，2019年1月25日
  8. 粗幾何学における非正曲率空間の新しい定式化とその境界
    日本数学会年会・幾何学分科会　東京大学　2018年3月18日
  9. A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture
    1. Workshop: Non-Positively Curved Groups and Spaces Universität Regensburg, September 19, 2017 slide
    2. Noncommutative Geometry and K-Theory at Rits -The Fourth China-Japan Conference- Ritsumeikan University, March 28, 2018 slide
  10. 粗Cartan-Hadamard定理と粗Baum-Connes予想への応用
    1. 幾何学セミナー，首都大学東京，2017年7月21日
    2. 微分トポロジーセミナー，京都大学，2017年11月7日
  11. The coarse Baum-conjecture for product of nonpositive curved spaces and groups
    1. 首都大学東京　幾何学セミナー，2016年4月15日
    2. Workshop on Development of new methods in Symplectic Geometry: JSPS Bilateral Joint Research Project between Belgium and Japan, 東北大学，2016年4月26日
    3. 慶應義塾大学　幾何学セミナー，2016年5月9日
    4. Glances@Manifolds II, Jagiellonian University in Kraków,August 8-13, 2016, Kraków, Poland
    5. the second China-Japan geometry conference, September 10, 2016, Fujian Normal University, 中国福建省福州市
  12. 非正曲率を持つ群の直積に対する粗Baum-Connes予想
    松山TGSAセミナー，愛媛大学，2016年9月26日
  13. Small cancellation 理論について
    Osajda's monster 勉強会，ルネッサ赤沢（伊東市），2016年1月4日
  14. Boundary of relatively hyperbolic groups and coarse geoemtry
    日中非可換幾何学研究集会，重慶大学，2015年12月21日
  15. 相対双曲群の境界と粗幾何学
    日本数学会秋季総合分科会特別講演，京都産業大学，2015年9月16日
  16. 幾何学的群論の紹介
    数学の魅力, 東北大学, 2014年12月14日
    学部生向けに，自身の研究内容に触れながら講演をおこなった．
  17. Coarse Baum-Connes conjecture for product spaces
    確率論と幾何学, 東京工業大学, 2014年9月24日
  18. 直積空間の境界とCoarse Baum-Connes 予想
    第61回幾何学シンポジウム, 名城大学, 2014年8月24日
  19. 境界とCoarse Baum-Connes予想
    幾何学セミナー, 東北大学, 2014年6月17日
  20. Blow up of the boundary of relatively hyperbolic group
    Rigidity school,　東京大学, 2013年1月8日．
  21. "Coarse Baum-Connes conjecuture for relatively hyperbolic groups"
    1. General and Geometric Topology and its Applications, Kyoto university, Oct 18 2011.
    2. 4th Doctorial Forum of Mathematics between Fudan and Kyoto Universities, Fudan university, Nov 1 2011.
    3. The 4th GCOE International Symposium on ``Weaving Science Web beyond Particle-Matter Hierarchy'' Tohoku universities, Sendai, February 21 2012.
    4. Group actions and K-theory, Kyoto university, Kyoto, March 12 2012.
    5. 日本数学会年会, 東京理科大学, 2012年3月26日
    6. 幾何学シンポジウム，九州大学，2012年8月27日
    7. 幾何学セミナー，東北大学，2012年10月9日
    8. 幾何学セミナー，名古屋大学，2012年11月13日
    9. Séminaire d'Algèbr d'Opérateur, Institut de Mathématiques, Université Paris 7, 18 Avril
    10. Darboux seminar, Institut de Mathématiques, Université Montpellier 2, 18 Octobre, 2013
    11. Séminaire Caen Cergy Clermont Paris, Institut de Mathématiques, Université Paris 7, 13 Decembre , 2013
  22. "相対双曲群のMayer-Vietoris完全列とNovikov予想",
    幾何学セミナー 九州大学, 2011年7月8日
  23. "Fixed point theorem on the Higson corona",
    Geometry and Analysis, Kyoto Universities, March 9 2011.
  24. "Coarse geometry and topology of Higson corona",
    1. 一般位相幾何学及び幾何学的トポロジーの最近の話題とその応用, 数理解析 研究所, 2010年10月13日
    2. 河野明先生還暦記念研究集会，城崎，2010年12月4日
    3. 愛媛大学談話会，愛媛大学，2010年12月8日
  25. "Dynamical Morse inequality",
    MSJ Autumn Meetings, held at Nagoya university, Septmeber 23,2010.
  26. "Euclidean cones of Sublinear Higson coronae",
    1. Differential topology seminar, held at Kyoto university, April 27,2010.
    2. Geometry and Probability, held at Tohoku university, August 27, 2010.
  27. "Toward the Homotopy theory on the Higson corona",
    新たな幾何学探索勉強会in松島, 松島, 2010年3月18日
  28. "Coarse Geometry, Higson compactification and fixed point property",
    1. Differential topology seminar, held at Kyoto university, January 13 2009.
    2. International Workshop on Noncommutative Geometry and Physics, 2009, held at Keio University, February 18-21, 2009
    3. Student colloquium, at Osaka City university, February 12, 2009
    4. Geometry Symposium, at Saga university, August 28
    5. Discrete Geometry related to Groups and Dynamics, at Ehime university, August September 2-3, 2009
    6. Séminaires de Analyse et Géométrie, Institut de Mathématiques de Jussieu, October 15
    7.First friendship meeting in mathematics betwwheen Fudan and Kyoto University, held at Kyoto, 11-15 Jan. 2010.
  29. "Introduction to Coarse Geometry",
    at Coarse Geometry school, held at Yokohama city, December 10-12 2008.
    M.Tsukamoto and I gave a three days lectures on the Coarse geometry. Coarse geometry is the study of global structure of non-compact spaces by looking the spaces coarsely. From this view point, we see that R(real numbers) and Z(integers) are "same" spaces. Surprisingly, "coarse structure" can be defined on a space even if which is NOT a metric space. It is an analogy to the fact that "local structure",that is, "topology", can be defined on a space even if which is not a metric space. The topological space equipped with a coarse structure which is compatible with its topology is called proper coarse space. The most typical proper coarse spaces is proper metric spaces.
    There is a compactification of a proper coarse space called Higson compactification. It's boundary, called Higson corona, seems to have rich data of the infinity of the space. Unfortunately, Higson corona of a proper metric space can never be metrizable. A group action on a coarse space induces a group action on a Higson corona. The fixed point theorem on a action of an abelian group on a Higson corona is given by myself.
    Coarse cohomology is defined for a coarse space in the similar way to the Alexander-Spanier cohomology for a topological space. It seems that coarse cohomology play an important role in the index theorem for non compact Riemannian manifold.
  30. "Asymptotic distribution of critical values", joint work with M.Tsukamoto,
    1. 3rd Lusternik-Schnirelmann category symposium, held at Karatsu Saga prefecture,October 29 2008.
    2. Differential topology seminar,held at Kyoto university,May 26 2009.
    3. Geometry and Analysis, Grands Moulins, Paris, December 23 2009.
  31. "Computer Algebra and Algebraic Topology", at First Global COE Seminar on Mathematical Research Using Computers, held at Kyoto university, October 24 2008. Quick Time Movie, PDF
  32. "Application of non-commutative Groebner Bases to calculations of E_2 terms of the Adams spectral sequence",
    1.The 4th COE Conference for Young Researchers, held at Hokkaido university, February 12 2008. PDF
    2. Kyoto seminar on algebraic topology in honor of Moo Ha Woo, held at Kyoto university, March 14-15 2008;
    3. Homotopy seminar,held at Kyushu university,March 26-27 2008;
  33. "Application of Groebner basis to computing some homotopy invariants", at Johns Hopkins University Topology Seminar, held at Johns Hopkins University, November 14 2007. PDF
  34. "Immersion problem of oriented Grassmann manifolds", at Takamatsu seminar on homotopy theory, held at Takamatsu National College of Technology, March 2007.
  35. "Groebner basis and cohomology of oriented Grassmann manifolds with application of LS-category", at The 3rd COE Conference for Young Researchers, held at Hokkaido university, February 2007.
  36. "Computing the cup-length of oriented Grassmann manifolds using Groebner basis", at 2nd Lusternik-Schnirelmann category symposium, held at Karatsu Saga prefecture, October 2006.

Expository Articles

(in Japanese)
[1] Tomohiro Fukaya, Application of Groebner basis for algebraic topology, 2007

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