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，集中講義，数学の話題，大学院進学について)

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

1. arXiv:2302.01017 (with D. Kishimoto and M. Takeda)
   The space of commuting elements in a Lie group and maps between classifying spaces,
   preprint.
2. arXiv:2211.00512 (with T. Kato and D. Kishimoto)
   Vector fields on non-compact manifolds,
   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:2101.10596 (with S. Hasui, D. Kishimoto and M. Takeda)
   Tverberg's theorem for cell complexes,
   accepted for publication in Bull. Lond. Math. Soc.

1. arXiv:2102.00606 (with T. Kato and D. Kishimoto)
   Homotopy type of the unitary group of the uniform Roe algebra on Zⁿ,
   J. Topol. Anal. 15 (2023), 495-512.
2. arXiv:2007.06787 (with T. Kato and D. Kishimoto)
   Homotopy type of the space of finite propagation unitary operators on Z,
   Homology, Homotopy Appl. 25 (2023), 375-400.
3. arXiv:2111.15096
   Higher homotopy normalities in topological groups,
   J. Topol. 16 (2023), 234-263.
4. arXiv:2012.15372 MR4527556 (with M. Tsukamoto and M. Yoshinaga)
   G-index, topological dynamics and marker property,
   Israel J. Math. 251 (2022), 737-764.
5. MR4129805 (with N. Iwase)
   Upper bound for monoidal topological complexity,
   Kyushu J. Math. 74 (2020), 197-200.
6. arXiv:1807.02944 MR3975098 (with N. Iwase and M. Sakai)
   A short proof for tc(K)=4,
   Topology Appl. 264 (2019), 167-174.
7. 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.
8. MR3811091
   Corrigendum to `Homotopy pullback of A_n-spaces and its applications to A_n-types of gauge groups' [Topology Appl. 187 (2015) 1–25],
   Topology Appl. 243 (2018), 159-162.
9. 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.
10. MR3679077 (with D. Kishimoto and S. Theriault)
    The homotopy types of G₂ gauge groups,
    Topology Appl. 228 (2017), 92-107.
11. arXiv:1408.2010 MR3491849
    Mapping spaces from projective spaces,
    Homology, Homotopy Appl. 18 (2016), 173-203.
12. MR3465846 arXiv:1502.02781 (with D. Kishimoto)
    Infiniteness of A_∞-types of gauge groups,
    J. Topol. 9 (2016), 181-191.
13. arXiv:1210.8252 MR3327166 !!Erratum!!
    Homotopy pullback of A_n-spaces and its applications to A_n-types of gauge groups,
    Topology Appl. 187 (2015), 1-25.
    
14. 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.
15. 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.
16. MR3071142 (with D. Kishimoto and A. Kono)
    Mod p decompositions of gauge groups,
    Algebr. Geom. Topol. 13 (2013), 1757-1778.
17. arXiv:1107.3908 MR2876314
    Finiteness of A_n-equivalence types of gauge groups,
    J. London Math. Soc. 85 (2012), 142-164.
18. 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.

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

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

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

1. Slides
   Higher homotopy normalities in topological groups,
   Topology Symposium, Nara Women's University, August 2023.
2. Slides
   An associative model of homotopy coherent functors and natural transforamations,
   Kansai Algebraic Topology Seminar, Osaka Metropolitan University, February 2023.
3. Finite propagation operators and Hilbert bundles with end,
   Topology Seminar, the University of Aberdeen, September 2022.
4. 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.
5. Slides
   Homotopy normalities in topological groups,
   Kyoto-Kyushu-Shinshu Topology Joint Seminar, online, December 2021.
6. Slides
   Finite propagation operators and Hilbert bundles with end,
   TMU Geometry Seminar, online, Tokyo Metropolitan University, June 2021.
7. Slides
   Homotopy type of the space of finite propagation unitary operators on Z,
   Southampton-Kyoto Workshop II, online, December 2020.
   
8. Slides
   Homotopy types of spaces of finite propagation unitary operators on Z,
   WORKSHOP: unitary operators: spectral and topological properties, online, September 2020.
   
9. 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.
   
10. Characterizations of homotopy fiber inclusion,
    Homotopy Theory Symposium, Hokkaido University, October 2019.
11. Reidemeister trace and Pontryagin-Thom construction,
    Reidemeister traces and gauge theory, the University of Ryukyus, October 2019.
12. 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.
13. Slides
    Homotopy theory of A_n-spaces in Lie groups,
    Colloquium, Kyoto University, June 2019.

Talks 2014-2018

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 2025

- 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

- Linear Algebra I, First Semester 2023

- Exercise of Mathematics AI (linear algebra and calculus), First Semester 2023

- Advanced Linear Algebra, First Semester 2023

- Calculus II, Second Semester 2022

- Core Seminar II (seminar for 1st year undergraduate students), Second Semester 2022

- 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