研究 (Research)

Publications

1. Bubbletons and their parallel surfaces in Euclidean 3-space, EG-Models numbered 2002.03.001

2. Bubbletons in hyperbolic 3-space and spherical 3-space, EG-Models numbered 2002.03.002

3. Bubbleton surfaces in 3-dimensional space forms, Balkan Journal of Geometry and its Applications,   9 (2004), no. 1, 46--72. 

4. Loop group methods for constant mean curvature surfaces (with S. Fujimori, W. Rossman), Rokko Lectures in Mathematics 17, 2005.

5. Characterizations of Bianchi-Baecklund transformation of constant mean curvature surfaces (with  J. Inoguchi), International Journal of Mathematics, 16 (2005), no. 2, 101--110. 

6. Constant mean curvature surfaces of any positive genus (with M. Kilian, W. Rossman, N. Schmitt), Journal of the London Mathematical Society, (2) 72 (2005), no. 1, 258--272.

7. Coarse classification of constant mean curvature cylinders (with J. Dorfmeister), Transactions of the American Mathematical Society, 359 (2007), no. 6, 2483--2500. 

8. Differential Geometry of surfaces and Soliton equations, in Japanese (with J. Inoguchi, N. Matsuura), Rikkyo Lecture note No. 8，2005 February.

9. Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms (N. Schmitt, M. Kilian, S.-P. Kobayashi, W. Rossman), Journal of the London Mathematical Society, (2) 75 (2007), no. 3, 563--581. 

10. Asymptotics of ends of constant mean curvature surfaces with bubbletons, Proceedings of the American Mathematical Society, 136 (2008), no. 4, 1433--1443. 

11. Note on equivariant harmonic maps in complex projective spaces, Annals of Global Analysis and Geometry, 36 (2009), no. 4, 375--380.

12. Real forms of complex surfaces of constant mean curvature, Transactions of the American Mathematical Society, 363 (2011), no. 4, 1765--1788.

13. Complex constant mean curvature surfaces fibered by minimal surfaces (with J. Dorfmeister, F. Pedit), Hokkaido Mathematical Journal, 39 (2010), no. 1, 1--55.

14. Constant mean curvature surfaces in hyperbolic 3-space via loop groups (with J. F. Dorfmeister, J. Inoguchi), Journal für die Reine und Angewandte Mathematik (Crelle's Journal), 686 (2014), 1-36.

15. Totally symmetric surfaces of constant mean curvature in hyperbolic 3-space, Bulletin of the Australian Mathematical Society, 82 (2010), no. 2, 240--253.

16. Discretization of integrable systems via dressing actions (in Japanese), RIMS Kokyuroku Bessatsu, B41 (2013), 148--161.

17. Constant Gaussian curvature surfaces in the 3-sphere via loop groups (with D. Brander, J. Inoguchi), Pacific Journal of Mathematics, 269 (2014), no. 2, 281--303.

18. A loop group method for minimal surfaces in the three-dimensional Heisenberg group (with J. F. Dorfmeister, J. Inoguchi), Asian Journal of Mathematics, 20 (2016), no. 3, 409--448.

19. A loop group method for Demoulin surfaces in the 3-dimensional real projective space, Differential Geometry and its Applications, 40 (2015), 57-–66.

20. On the Bernstein problem in the three-dimensional Heisenberg group via loop groups (with J. F. Dorfmeister, J. Inoguchi), Canadian Mathematical Bulletin, 59 (2016), no. 1, 50-–61.

21. A construction method for discrete constant negative Gaussian curvature surfaces, Mathematical Progress in Expressive Image Synthesis III, Extended and Selected Results from the Symposium MEIS2015, (2016), 21--33.

22. A loop group method for affine harmonic maps into Lie groups (with J. F. Dorfmeister, J. Inoguchi), Advances in Mathematics, 298 (2016), 207--253.

23. Nonlinear d'Alembert formula for discrete pseudospherical surfaces, Journal of Geometry and Physics, 119 (2017), 208--223.

24. General-affine invariants of plane curves and space curves (with T. Sasaki), Czechoslovak Mathematical Journal, 70 (2020), 67--104.

25. Survey on real forms of the complex A^(2)_2-Toda equation and surface theory (with J. F. Dorfmeister, W. Freyn, E. Wang), Complex Manifolds  6 (2019), no. 1, 194–227.

26. Representation formula for discrete indefinite affine spheres (with N. Matsuura), Differential Geometry and Its Applications, 69 (2020), 101592, 41 pp.

27. Ruh-Vilms theorems for minimal surfaces without complex points and minimal Lagrangian surfaces in CP^2 (with J. F. Dorfmeister, H. Ma), Mathematische Zeitschrift, 296 (2020), no. 3-4, 1751--1775.

28. Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space (with J. F. Dorfmeister),  Annali di Matematica Pura ed Applicata (1923 -), 200 (2021), 521--546.

29. The Gauss maps of Demoulin surfaces with conformal coordinates (with J. Inoguchi), SCIENCE CHINA Mathematics,  64 (2021), no. 7, 1479–1492.

30. A characterization of the alpha-connections on the statistical manifold of normal distributions (with J. Inoguchi, H. Furuhata), Information Geometry, 4 (2021), no. 1, 177–188.

31. On a constant curvature statistical manifold (with Y. Ohno),  Information Geometry,  5 (2022), no. 1, 31-46.

32. Timelike minimal surfaces in the three-dimensional Heisenberg group (with H. Kiyohara),  Journal of  Geometric  Analysis, 32 (2022), no. 8, Paper No. 225, 37 pp.

33. Discrete constant mean curvature surfaces on general graphs (with T. Hoffmann, Z. Ye),  Geometriae Dedicata,  216 (2022), no. 6, Paper No. 71.

34. Minimal surfaces with non-trivial topology in the three-dimensional Heisenberg group (with J. F. Dorfmeister, J. Inoguchi),  Complex Manifolds, 9 (2022), 285-336. 

35. Minimal cylinders in the three-dimensional Heisenberg group, Mathematische Annalen, 388 (2024), no.3, 3299-3317.

36. Geodesics of multivariate normal distributions and a Toda lattice type Lax pair, Physica Scripta, Volume 98(2023), Number 11.

37. A characterization of the alpha-connections on the statistical manifold of multivariate normal distributions (with Y. Ohno),  Osaka J. Math. 62 (2025), no2, 329–349.

38. Half-dimensional immersions into the para-complex projective space and loop group method (with J.-F. Dorfmeister, R. Hildebrand),  Results in Mathematics,  79 (2024), no. 7, Paper No. 245

39. The complex landslide flow and the method of integrable systems, IMRN 25(2025), no. 7, rnaf072

40. Maximal surfaces in the Lorentzian Heisenberg group (with D. Brander), Mathematical Proceedings of the Cambridge Philosophical Society, to appear.

41. The evolution of a curve induced by the Pohlmeyer-Lund-Regge equation (with Y. Kogo, N. Matsuura),  Journal of Nonlinear Science, Volume 35(2025), no. 4, Paper No. 85.

Preprints

  0. Constant mean curvature and constant Gauss curvature cylinders (with N. Schmitt), preprint.

1. A classification of constant Gaussian curvature surfaces in the three-dimensional hyperbolic space (with J.-I. Inoguchi), submitted, 2024.

2. Gauss maps of Möbius surfaces in the n-dimensional sphere (with D. Brander, P. Wang), submitted, 2024.

3. A duality for minimal surfaces in the Heisenberg group, submitted, 2025.

Misc

1. Asymptotics of dressed CMC surfaces, Surikaiseki Kenkyusho Kokyuroku (2003), 1346, 47-61.

2. Constant mean curvature surfaces in 3-dimensional space forms (with M. Kilian, W. Rossman, N. Schmitt), math.DG/0403366

3. Imperfect draft of a supplement for "Loop group methods for constant mean curvature surfaces" (with S. Fujimori, W. Rossman).

4. Complex constant mean curvature surfaces via integrable system methods, Oberwolfach report (2007), no. 24, 1318 -- 1322.

5. Delaunay surfaces via integrable system methods (with J. Dorfmeister, M. Schuster).

Talks

2025

1. 離散ガウス曲率負一定曲面のワイエルシュトラス型の表現公式, Workshop on Interaction of Robotic Surfaces and Discrete Differential Geometry , 北海道大学，January 23, 2025

2. The complex landslide flow via harmonic maps into hyperbolic two-space, YMSC Topology seminar, March 10, 2025

3. The complex landslide flow via harmonic maps into hyperbolic two-space, BIMSA Differential Geometry Seminar, March 11, 2025

4. Series of lectures about the generalized Weierstrass typre representations, Northeastern University China, March 3, 5, 7, 17, 19, 21, 24, 26, 28, 2025.

2024

1. Constant Gaussian curvature surfaces in the hyperbolic 3-space and an application to Teichmüller theory,  Surface Theory and Harmonic Maps, Technical University of Denmark August 12-17,  August 14, 2024 

2. The A_2^(2) Toda Equations, Affine Spheres, Minimal Surfaces, and Ruh–Vilms Type Theorems, Workshop on surface theory and harmonic maps, Fujian Normal University November 23-24, November 23, 2024

2023

1. Geodesics of multivariate normal distributions and a Toda lattice type Lax pair,  九州大学 第 9 回伊都 CREST ED3GE セミナー,  April 28, 2023 

2. A characterization of the alpha-connections on the statistical manifold of multivariate normal distributions, 千里山幾何学研究会, June 24, 2023

3.  Class A Bézier curve defined in the local coordinate system, CREST ED3GE戦略会議, December 17, 2023

2022

2021

1. The generalized Weierstrass type representation for surfaces (1), (2), The 13th MSJ-SI 2020Mathematical Society of Japan - Seasonal Institute Differential Geometry and Integrable Systems -Mathematics of Symmetry, Stability and Moduli-,  March 8, 2021

2020

1. 等質的な統計多様体について，ミニワークショップ 統計多様体の幾何学とその周辺 (12)， December 24, 2020

2019

1. 一般アフィン平面および空間曲線について，幾何学コロキウム，北海道大学, April 26, 2019

2. 不定値複素射影平面の時間的全実極小曲面について, 北九州幾何学研究集会 2019幾何研究会; 九州工業大学，July 7, 2019

2018

1. Loop group method for surfaces with constant Gaussian curvature in the 3-dimensional hyperbolic space,  Geometry of Submanifolds and Integrable Systems The 15th OCAMI-RIRCM Joint Differential Geometry Workshop & The 3rd OCAMI-KOBE-WASEDA Joint International Workshop on Differential Geometry and Integrable Systems On Occasion of Professor Yoshihiro Ohnita for his 60th Birthday; Osaka City University Osaka; March 29, 2018

2. A real form of a_2^(2) and timelike minimal Lagrangian surfaces, Geometry Seminar at University of Augsburg; May 14, 2018

3. A real form of a_2^(2) and timelike minimal Lagrangian surfaces, Integrable geometry at Bayrischzell; May 16, 2018

4. D'Alembert type representation for discrete surfaces, SFB Colloquium; Technical University of Berlin; July 3, 2018

5. Minimal surfaces in the 3-dimensional Heisenberg group, m:iv Summer 2018 Workshop, Technical University of Munich; August 21, 2018

6. General-affine invariants of plane curves and space curves, Differential Geometry in honor of Udo Simon's 80th birthday; September 8, 2018

7. 離散微分幾何学と可積分系, 日本数学会 北海道支部会，December 12, 2018

2017

1. Surfaces with constant Gaussian curvature in the 3-dimensional hyperbolic space via loop groups, Geometry colloquium; University of Massachusetts (Amherst), Amherst United States; March 27, 2017

2. A construction method for discrete indefinite affine spheres, The Tenth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory; University of Georgia, Athens United States; March 31, 2017

3. Minimal surfaces with symmetries in the three-dimensional Heisenberg group, Higgs Bundles, Harmonic Maps, and Integrable Systems" in honor of Franz Pedit's 60th birthday; Leibniz Universität Hannover, Hannover Germany; August 18, 2017

4. 3 次元ハイゼンベルグ群の極小曲面について I, II, 幾何学阿蘇研究集会; 休暇村 南阿蘇 熊本; September 27, 2017

2016

1. Nonlinear d'Alembert formula for discrete pseudospherical surfaces, OCAMI-KOBE-WASEDA Joint International Workshop on Differential Geometry and Integrable Systems; Kobe University, Kobe, Japan; February 16, 2016

2. 可積分の手法によるリー群への調和写像，第６３回幾何学シンポジウム; Okayama University, Okayama Japan; August 27, 2016.

3. Constant negative Gaussian curvature surfaces in the 3-dimensional hyperbolic space, One day workshop at Waseda Univeristy; Waseda University, Shinjuku, Japan; October 8, 2016.

4. A discrete version of the DPW method for discrete constant negative Gaussian curvature surfaces, Extra lectures by guest speakers for Dorfmeister's lectures; Waseda University, Shinjuku, Japan; October 10, 2016.

5. 平均曲率一定曲面に対するワイエルシュトラス型の表現公式（入門）,  幾何学コロキウム; Hokkaido Univerisity, Sapporo Japan; December 16, 2016.

2015

1. A construction method for discrete constant negative Gaussian curvature surfaces, MEIS2015; Kyushu University, Nishijin, Japan; September 26, 2015.

2014

1. 変数分離法による離散サインゴルドン方程式の解の構成法，九州可積分系セミナー; Kyushu University, Ito, Japan; February 21, 2014.

2. 離散可積分曲面論入門, 離散可積分系・離散微分幾何チュートリアル2014; Kyushu University, Ito, Japan; February 23, 2014.

3. Poisson's equations for inhomogeneous dielectric materials and neutral harmonic maps, PDEセミナー; Hokkaido University, Sapporo, Japan; April 17, 2014.

4. A loop group method for affine harmonic maps into Lie groups, RIMS研究集会 「群作用と部分多様体論の展開; Kyoto Japan; June 26, 2014.

5. デモラン曲面のガウス写像による特徴付けについて; 関大微分幾何研究会; Kansai University, Suita Japan; July 6, 2014.

6. ３次元ハイゼンベルグ群内の極小曲面について; 部分多様体とリー群作用2014; Tokyo University of Science, Kagurasaka Japan; September 6, 2014.

7. 双曲平面への調和写像と曲面論への応用, 幾何学コロキウム; The University of Tokyo, Meguro Japan; November 7, 2014.

2013

1. 曲面のワイエルシュトラス型の表現公式について, 幾何学コロキウム; Hokkaido University, Sapporo, Japan; July 12, 2013.

2. 曲面の幾何学について，談話会；Hokkaido University, Sapporo, Japan; October 3, 2013.

3. さまざまな空間の曲面のワイエルシュトラス型の表現公式について，広島幾何学研究集会2013；Hiroshima University, Higashi-Hiroshima; October 11, 2013.

4. 可積分系の手法による極小曲面の構成法について, 二国間共同研究：極小曲面セミナー；Tokyo Institute of Technology, Meguro, Japan; October 25, 2013.

5. 離散ガウス曲率負一定曲面について，進展する曲面論-Advances in Surface Theory-; Yamaguchi University, Yamaguchi, Japan; December 27, 2013.

2012

1. Harmonic trinoids in complex projective spaces, Isomonodromic deformations and related topics; Tokyo Metropolitan University, Minami-Ohsawa, Japan; January 27, 2012.

2. ハイゼンベルグ群内の平均曲率一定曲面について, つくば幾何学小研究会; Tsukuba University, Ibaraki, Japan; February 15, 2012.

3. 三次元ハイゼンベルグ群内の平均曲率一定曲面について, ３月曲面論小研究集会; Tokyo Institute of Technology, Meguro, Japan; March 19, 2012.

4. 三次元ハイゼンベルグ群内の平均曲率一定曲面について, 日本数学会2012年度年会; Tokyo Sience University, Kagurazaka, Japan; March 26, 2012.

5. ループ群による３次元双曲空間内の平均曲率一定曲面について, 名古屋大学; Nagoya University, Nagoya, Japan; August 8 -- August 10, 4回 ×90分.

6. Dressing 作用による可積分系の差分化について, 離散可積分系の拡がり; 数理解析研究所; Kyoto, Japan; August 22, 2012.

2011

1. A classification of equivariant constant Gauss curvature and constant mean curvature cylinders, The 4th International Workshop on Nonlinear Mathematical Physics and The 11th National Conference on Integrable Systems; Wuhan Institute of Physics and Mathematics, Wuhan, China; July 27, 2011.

2. Minimal surfaces in hyperbolic three-space, Geometry Seminar, Tsinghua University, Beijing, China; August 1, 2011.

3. 可積分曲面へのループ群作用, 2011 Geometry Symposium (第58回幾何学シンポジウム); Yamaguchi University, Yamaguchi, Japan; August 29, 2011.

4. 可積分系の手法を用いた双曲空間内の平均曲率一定曲面の構成について, 弘前非線形方程式研究会; Hirosaki University, Hirosaki, Japan; December 23, 2011.

2010

1. Constant mean curvature surfaces in H^3 via integrable system methods, Progress in Surface Theory; Oberwolfach Mathematical Institute, Oberwolfach, Germany; May 6, 2010.

2. Dressing action on complex CMC surfaces and real forms, Oberseminar Differentialgeometrie; Universitat Augsburg, Augsburg, Germany; July 2, 2010.

3. Constant Gauss Curvature Cylinders, Submanifold Geometry and Lie Group Actions; Tokyo University of Science, Kagurazaka, Japan; September 9, 2010.

2009

1. 複素平均曲率一定曲面と実形, 2009年度日本数学会年会; Tokyo University, Komaba, Japan; March 28, 2009.

2. Harmonic trinoids in complex projective spaces, Fusion of Integrable Systems and Geometry; Tohoku University, Sendai, Japan; April 19, 2009.

3. Surveys of integrable surfaces, GEOSOCK seminar; Osaka City University, Umeda, Japan; May 13, 2009.

4. Global solutions of elliptic (G, rho)-systems, New aspects of surface theory; Tokyo Metropolitan University, Hachioji, Japan; May 15, 2009.

2008

1. H^3内の平均曲率一定曲面のワイエルシュトラス型の表現公式について, 幾何学セミナー; Nagoya University, Nagoya, Japan; July 1, 2008.

2. Harmonic trinoids in CP^n, 弘前幾何学セミナー; Hirosaki University, Hirosaki, Japan; August 26, 2008.

3. Harmonic trinoids in complex projective spaces,Integrable systems, Geometry and Visualization 2008; Kyushu University, Hakozaki, Japan; December 12, 2008.

2007

1. Complex Constant Mean Curvature Surfaces via integrable system methods, Progress in Surface Theory; Oberwolfach Mathematical Institute, Oberwolfach, Germany; April 30, 2007.

2. 複素平均曲率一定曲面の実形について, Differential Geometry Seminar (微分幾何学セミナー); Tsukuba University, Ibaraki, Japan; June 5, 2007.

3. Real form surfaces of a complex constant mean curvature surface, 可積分系に関わる幾何学, 平成１９年９月２５日（火）-２８ 日（金); RIMS, Kyoto, Japan; September 27, 2007.

4. 一般超幾何関数のモノドロミー群を用いたCPnの調和写像の構成について, アクセサリー・パラメーター研究会 2007; Kumamoto University, Kumamoto, Japan; October 8, 2007.

5. H3内の平均曲率一定曲面の構成について, 部分多様体論・湯沢 (湯沢研究会); Yuzawa Grand Hotel, Niigata, Japan; November 23, 2007.

6. H^3内の平均曲率一定曲面のワイエルシュトラス型の表現公式について, Kyushu Geometry Seminar (幾何学セミナー); Kyushu University, Hakozaki, Japan; December 21, 2007.

2006

1. Constant Mean Curvature Surfaces with bubbletons, Geometry, Integrable Systems and Visualization; Osaka City University, Osaka, Japan; January 26, 2006.

2. 平均曲率一定曲面と可積分系の関係について, Toda seminar; Tokyo University, Tokyo, Japan; June 17, 2006.

3. 平均曲率一定曲面と線形常微分方程式について, アクセサリー・パラメーター研究集会; Kumamoto University, Kumamoto, Japan; June 22, 2006.

4. Integrable surfaces via complex constant mean curvature immersions, Conference on London Mathematical Society Durham Symposium, "Methods of Integrable Systems in Geometry", Friday 11th August - Monday 21st August 2006 (Informal programme); University of Durham, Durham, England; August 18, 2006.

2005

1. Complex constant mean curvature surfaces fibered by minimal surfaces, Differential Geometry Seminar (微分幾何学セミナー); Tsukuba University, Ibaraki, Japan; March 1, 2005.

2. 可積分系の方法による平均曲率一定曲面の一般化について, 名城大学 第2回 幾何学研究集会, 部分多様体の幾何学的諸相; Meijo University, Nagoya, Japan; March 15, 2005.

3. CMCLab tutorial, CMCLab tutorial; Tokyo Metropolitan University, Hachioji, Japan; June 30, 2005.

4. Complex Constant Mean Curvature Surfaces fibered by minimal surfaces, Kuju Geometry Symposium; Kuju, Ohita, Japan; September 10, 2005.

5. Constant Mean Curvature Surfaces via Integrable system methods, Kumamoto University Geometry Seminar; Kumamoto University, Kumamoto, Japan; December 5 -- 6, 2005.

6. Coarse classification of constant mean curvature cylinders, Osaka City University Differential Geometry Seminar; Osaka City University, Osaka, Japan; December 7, 2005.

7. Loop groups and surface theory, 多様体上の微分方程式; Kanazawa University Satellite Plaza, Kanazawa, Japan; December 12, 2005.

2004

1. Complex ODE's and Surfaces of Constant Mean Curvature, DFG-Schwerpunkt-Kolloquium, University of Leipzig, Germany; July 27, 2004.

2. Coarse Classification of Constant Mean Curvature Cylinders, 2004 Geometry Symposium (第51回幾何学シンポジウム); Tokyo Metropolitan University, Hachioji, Japan; August 8, 2004.

3. Bianchi-Baecklund and Darboux Transformations on CMC Surfaces, 2004 Mathmatical Society of Japan fall meeting (日本数学会2004年度秋季総合分科会); Hokkaido University, Hokkaido, Japan; September 20, 2004.

4. CMC-Lab tutorials, Tutorial for Graduate Students on International workshop, Integrable Systems, Geometry and Visualization (国際研究集会 Integrable systems, Geometry and Visualization); Kyushu University, Fukuoka, Japan; November 20, 2004.

5. Bianchi-Baecklund and Darboux transformations on CMC surfaces (平均 曲率一定曲面に対するBianchi-Baecklund変換とDarboux変換について), Submanifolds in YUZAWA 2004, (部分多様体論, 湯沢2004); Yuzawa Grand Hotel, Niigata, Japan; December 2, 2004.

6. Coarse classification of CMC-cylinders, Differential Geometry of surfaces with singularities (特異点をもつ曲面の微分幾何学的研究) ; Research Institute for Mathematical Sciences, Kyoto, Japan; December 22, 2004.

7. Bubbletons and simple-type dressing, Conference on Mathematical Visualization; Tokyo Metropolitan University, Hachioji, Japan; January 21, 2003.

8. CMC Lab, Java View による曲面の視覚化, OpenXM committers meeting; Kanazawa University, Ishikawa, Japan; February 13, 2003.

9. Bubbleton曲面の漸近挙動について, 等質空間と部分多様体の幾何学; Research Institute for Mathematical Sciences at Kyoto; Kyoto, Japan ; June 24, 2003.

2002

1. Bubbletons in 3-dimensional space forms via the DPW method, 2001年度 筑波大学微分幾何学研究集会; Tsukuba University, Ibaraki, Japan; February 22, 2002.

2. Constant Gauss Curvature Surfaces, Harmonic maps, minimal surfaces and geometric flows; University of Brest, Brest, France; July 8, 2002.

3. DPWの方法による空間形式内のGauss曲率一定曲面について, 第49回幾何学シンポジウム; Osaka University, Osaka, Japan; July 30, 2002.

4. DPWの方法による空間形式内のGauss曲率一定曲面について, 日本数学会2002年度秋季総合分科会; Shimane University, Shimane, Japan; September 27, 2002.

5. 可積分系の方法による３次元空間形内の平均曲率一定曲面とガウス曲率一定曲面, Geometry colloquium; Hokkaidou University, Hokkaidou, Japan; November 27, 2002.

6. 3次元空間形内のガウス曲率一定曲面(K>0)の特異点について, Singularity seminar; Hokkaidou University, Hokkaidou, Japan; November 28, 2002.

7. DPW-method for constant Gaussian curvature surfaces in space forms, Integrable curves and surfaces in 3-dimensional space forms; Utsunomiya University, Utsunomiya, Japan; December 5, 2002.

Conferences

1. 部分多様体の微分幾何学の深化, RIMS, 6/24--6/26, 2013

2. Oktoberfest! Dorfmeister's Lectures, 10, 2016

3. Integrable Geometry at Bayrischzell, 5/15--5/18, 2018

4. Geometry of surfaces at Hokkaido, 10/15--10/16, 2018

5. Geometric design meeting at Hokkaido, 10/16--10/17, 2018