Mitsunobu TSUTAYA

Faculty of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan.

tsutaya_at_math_dot_kyushu-u.ac_dot_jp (replace "_at_" with "@" and "_dot_" with ".")

I am the organizer of the Kyushu University Topology Seminar (Fridays 16:00-17:00).

学生向け情報 (講義,少人数セミナー,集中講義等)

Research Interest

algebraic topology, An-spaces, higher homotopy, mapping spaces, homotopy theory of Lie groups

Preprints

  1. arXiv:2211.00512 (with T. Kato and D. Kishimoto)
    Vector fields on non-compact manifolds,
    preprint.
  2. arXiv:2111.15096
    Higher homotopy normalities in topological groups,
    preprint.
  3. arXiv:2105.02981 (with T. Kato and D. Kishimoto)
    Hilbert bundles with ends,
    accepted for publication in J. Topol. Anal.
  4. arXiv:2103.12403 (with H. Maruhashi)
    De Rham cohomology of the weak stable foliation of the geodesic flow of a hyperbolic surface,
    preprint.
  5. arXiv:2102.00606 (with T. Kato and D. Kishimoto)
    Homotopy type of the unitary group of the uniform Roe algebra on Zn,
    accepted for publication in J. Topol. Anal.
  6. arXiv:2101.10596 (with S. Hasui, D. Kishimoto and M. Takeda)
    Tverberg's theorem for cell complexes,
    preprint.
  7. arXiv:2012.15372 (with M. Tsukamoto and M. Yoshinaga)
    G-index, topological dynamics and marker property,
    accepted for publication in Israel J. Math.
  8. arXiv:2007.06787 (with T. Kato and D. Kishimoto)
    Homotopy type of the space of finite propagation unitary operators on Z,
    accepted for publication in Homology, Homotopy Appl.

Published Papers

  1. MR4129805 (with N. Iwase)
    Upper bound for monoidal topological complexity,
    Kyushu J. Math. 74 (2020), 197-200.
  2. arXiv:1807.02944 MR3975098 (with N. Iwase and M. Sakai)
    A short proof for tc(K)=4,
    Topology Appl. 264 (2019), 167-174.
  3. arXiv:1612.08816 MR3852292 (with S. Hasui and D. Kishimoto)
    Higher homotopy commutativity in localized Lie groups and gauge groups,
    Homology, Homotopy Appl. 21 (2019), 107-128.
  4. MR3811091
    Corrigendum to `Homotopy pullback of An-spaces and its applications to An-types of gauge groups' [Topology Appl. 187 (2015) 1–25],
    Topology Appl. 243 (2018), 159-162.
  5. arXiv:1405.0337 MR3733837 (with D. Kishimoto)
    Samelson products in p-regular SO(2n) and its homotopy normality,
    Glasg. Math. J. 60 (2018), 165-174.
  6. MR3679077 (with D. Kishimoto and S. Theriault)
    The homotopy types of G2 gauge groups
    ,
    Topology Appl. 228 (2017), 92-107.
  7. arXiv:1408.2010 MR3491849
    Mapping spaces from projective spaces,
    Homology, Homotopy Appl. 18 (2016), 173-203.
  8. MR3465846 arXiv:1502.02781 (with D. Kishimoto)
    Infiniteness of A-types of gauge groups,
    J. Topol. 9 (2016), 181-191.
  9. arXiv:1210.8252 MR3327166 !!Erratum!!
    Homotopy pullback of An-spaces and its applications to An-types of gauge groups,
    Topology Appl. 187 (2015), 1-25.
  10. MR3194181 (with D. Kishimoto and A. Kono)
    On localized unstable K1-groups and applications to self-homotopy groups,
    Canad. Math. Bull. 57 (2014), 344-356.
  11. MR3164541 (with D. Kishimoto and A. Kono)
    On p-local homotopy types of gauge groups,
    Proc. Roy. Soc. Edinburgh: Sect. A 144 (2014), 149-160.
  12. MR3071142 (with D. Kishimoto and A. Kono)
    Mod p decompositions of gauge groups
    ,
    Algebr. Geom. Topol. 13 (2013), 1757-1778.
  13. arXiv:1107.3908 MR2876314
    Finiteness of An-equivalence types of gauge groups,
    J. London Math. Soc. 85 (2012), 142-164.
  14. arXiv:1101.4278 MR2864856
    A note on homotopy types of connected components of Map(S4,BSU(2)),
    J. Pure and Appl. Algebra 216 (2012), 826-832.

Unpublished papers

  1. arXiv:1606.07363
    Coincidence Reidemeister trace and its generalization,
    preprint.

Lecture Notes

  1. Evaluation fiber sequence and homotopy commutativity,
    lecture notes for Algebraic Topology Workshop for Young Researches 2015.

Other Documents

  1. M. Tsutaya,
    Results in Homotopy Theory of Gauge Groups (last update: Feb. 13, 2022).
  2. M. Tsutaya,
    On evaluation fiber sequences,
    RIMS Kokyuroku No. 1922, The Topology and the Algebraic Structures of Transformation Groups, 166-169.
  3. 井澤昇平・大下達也・蔦谷充伸・野坂武史,
    代数的K-理論の基礎とその周辺 (Japanese),
    第六回琵琶湖若手数学者勉強会(2012年2月)報告書
  4. 伊藤哲也・今城洋亮・蔦谷充伸・野坂武史,
    Atiyah-Singer の指数定理 (Japanese),
    第五回琵琶湖若手数学者勉強会(2011年2月)報告書

Talks 2019-

  1. Finite propagation operators and Hilbert bundles with end,
    Topology Seminar, the University of Aberdeen, September 2022.
  2. Slides
    Higher homotopy normalities in topological groups,
    Classifying spaces in homotopy theory: in honour of Ran Levi's 60th Birthday, ICMS, Bayes Centre, the University of Edinburgh, September 2022.
  3. Slides
    Homotopy normalities in topological groups,
    Kyoto-Kyushu-Shinshu Topology Joint Seminar, online, December 2021.
  4. Slides
    Finite propagation operators and Hilbert bundles with end,
    TMU Geometry Seminar, online, Tokyo Metropolitan University, June 2021.
  5. Slides
    Homotopy type of the space of finite propagation unitary operators on Z,
    Southampton-Kyoto Workshop II, online, December 2020.
  6. Slides
    Homotopy types of spaces of finite propagation unitary operators on Z,
    WORKSHOP: unitary operators: spectral and topological properties, online, September 2020.
  7. Slides
    Unstable homotopy types of spaces of finite propagation unitary operators on Z,
    joint seminar of Kansai gauge theory seminar and Kyoto algebraic topology seminar, online seminar, May 2020.
  8. Characterizations of homotopy fiber inclusion,
    Homotopy Theory Symposium, Hokkaido University, October 2019.
  9. Reidemeister trace and Pontryagin-Thom construction,
    Reidemeister traces and gauge theory, the University of Ryukyus, October 2019.
  10. Slides
    De Rham cohomology of the weak stable foliation of the geodesic flow of a hyperbolic surface,
    Topological Studies around Riemann Surfaces, the University of Tokyo, September 2019.
  11. Slides
    Homotopy theory of An-spaces in Lie groups,
    Colloquium, Kyoto University, June 2019.

Talks 2014-2018

Curriculum Vitae

Profesional experience

- Associate Professor, Kyushu Uniersity, Apr 2021 - present

- Assistant Professor, Kyushu Uniersity, May 2016 - Mar 2021

- JSPS Research Fellow PD, Kyushu University, April 2016

- Research Associate, Kyoto University, April 2013 - May 2016

- JSPS Research Fellow PD, Kyoto University, December 2011 - March 2013

- JSPS Research Fellow DC1, Kyoto University, April 2010 - November 2011

Organizing seminars and conferences

- Homotopy Theory Symposium, November 2021

- Homotopy Theory Symposium, November 2020

- Kyushu University Topology Seminar - organizer, April 2017 - present

Degrees

- D.S., Kyoto University, November 2011

- M.S., Kyoto University, March 2010

Grants

- Grant-in-Aid for Scientific Research (C) , Japan Society for the Promotion of Science, April 2022 - March 2024

- Grant-in-Aid for Early-Career Scientists, Japan Society for the Promotion of Science, April 2019 - March 2022

- Grant-in-Aid for Young Scientists (B), Japan Society for the Promotion of Science, April 2016 - March 2019

- Grant for Basic Science Research Projects, Sumitomo Foundation, November 2015 - November 2016

- Grant-in-Aid for JSPS Fellows, Japan Society for the Promotion of Science, April 2010 - March 2013

Teaching experience

- Calculus I, First Semester 2022

- Advanced Linear Algebra, First Semester 2022

- Basics of Topology (singular homology for graduate students), Second Semester 2021

- Core Seminar II (seminar for 1st year undergraduate students), Second Semester 2021

- Calculus III, First Semester 2021

- Exercise of Mathematics II (linear algebra and vector calculus), First Semester 2021

- Geometry II Exercise (homology of topological spaces), Second Semester 2020

- Geometry II Exercise (homology of topological spaces), Second Semester 2019

- Geometry I Exercise (manifolds), First Semester 2019

- Calculus III, First Semester 2019 (2 classes)

- Geometry II Exercise (homology of topological spaces), Second Semester 2018

- Calculus II, Second Semester 2018

- Geometry I Exercise (manifolds), First Semester 2018

- Calculus I, First Semester 2018

- Geometry II Exercise (homology of topological spaces), Second Semester 2017

- Geometry I Exercise (manifolds), First Semester 2017

- Survey in Mathematics II Exercise (metric spaces), First Semester 2017

- Linear Algebra, First Semester 2017

- Survey in Mathematics III Exercise (general topology), Second Semester 2016

- Survey in Mathematics I Exercise (convergence of series and sequence of functions), First Semester 2016