Japanese version here

List of Papers

1. Complete list of connection relations for Gauss hypergeometric differential equation, Kumamoto J. Math. 35 (2022), 1-60.
2. On Oshima's middle convolution, Josai Mathematical Monographs, 12 (2020), 19-51
3. Multiplicative middle convolution for KZ equations, Math. Z., 294 (2020), 1787-1839, DOI 10.1007/s00209-019-02322-9
4. Rigid Fuchsian systems in 2-dimensional conformal field theories (with Vladimir Belavin and Raoul Santachiara), Commun. Math. Phys., 365 (2019), 17-60, DOI 10.1007/s00220-018-3274-x
5. Three-dimensional representations of braid groups associated with some finite complex reflection groups (with Toshiya Matsumura), Int. J. Math., 28, 1750109 (2017) [44 pages].
6. Connection problem for regular holonomic systems in several variables, "Analytic, Algebraic and Geometric Aspects of Differential Equations", Trends in Mathematics, Birkhäuser, 2017, 337-350.
7. Holonomic Systems, "Analytic, Algebraic and Geometric Aspects of Differential Equations", Trends in Mathematics, Birkhäuser, 2017, 59-87.
8. Symmetric differential polynomials (with Kousuke Iida), Kumamoto J. Math., 30 (2017), 7-14.
9. Globally analyzable Fuchsian differential equations, Sugaku Expositions, 28 (2015), 49-72.
10. Rigidity of monodromies for Appell's hypergeometric functions (with Tatsuya Kikukawa), Opuscula Mathematica, 35 (2015), 567-594.
11. Prolongability of ordinary differential equations, Journal of Nonlinear Mathematical Physics, 20 Supplement 1 (2013), 70-84.
12. Regular coordinates and reduction of deformation equations for Fuchsian systems, Banach Center Publications, 97 (2012), 39-58.
13. Topological theory for Selberg type integral associated with rigid Fuchsian systems (with Sho Hamaguchi), Math. Ann. 353 (2012), 1239-1271.
14. Middle convolution for completely integrable systems with logarithmic singularities along hyperplane arrangements, Adv. Stud. Pure Math. 62 (2012), 109-136.
15. A connection problem for Simpson's even family of rank four (with Katsuhisa Mimachi), Funk. Ekvac. 54 (2011), 495-515. Correction
16. Generating systems for finite irreducible complex reflection groups (with Mitsuo Kato), Funk. Ekvac. 53 (2010), 435-488.
17. Studies on deformation of Fuchsian systems from the viewpoint of rigidity, RIMS Kokyuroku Bessatsu B5 (2008), 51-60.
18. Rigidity for Appell's hypergeometric series F₄ (with Youichi Ueno), Funk. Ekvac. 51 (2008), 149-164. Correction
19. Middle convolution and deformation for Fuchsian systems (with Galina Filipuk), J. London Math. Soc. 76 (2007), 438-450.
20. Construction of rigid local systems and integral representations of their sections (with Toshiaki Yokoyama), Math. Nachr. 279 (2006), 255-271.
21. On confluences of hypergeometric integrals, Kumamoto J. Math., 17 (2004), 1-8.
22. Evaluation of Stokes multipliers for a certain system of differential equations corresponding to a rigid local system, Funk. Ekvac. 46 (2003), 187-211.
23. Integral representations of solutions of differential equations free from accessory parameters, Adv. Math. 169 (2002), 187-240.
24. On rigidity of Pfaffian systems coming from Okubo systems (with Toshiaki Yokoyama), Kyushu J. Math. 55 (2001), 189-205.
25. Quadratic relations for confluent hypergeometric functions on Z_{2, n+1}, Funk. Ekvac. 42 (1999), 435-490.
26. Monodromy of an Okubo system with non-semisimple exponents, Funk. Ekvac. 40 (1997), 435-457.
27. Confluence of cycles for hypergeometric functions on Z_{2, n+1}, Trans. Amer. Math. Soc. 349 (1997), 675-712.
28. Irreducibility of accessory parameter free systems, Kumamoto J. Math. 8 (1995), 153-170.
29. Monodromy representations of systems of differential equations free from accessory parameters, SIAM J. Math. Anal. 25 (1994), 1595-1621.
30. Canonical forms of differential equations free from accessory parameters, SIAM J. Math. Anal. 25 (1994), 1203-1226.
31. Finite monodromy of Pochhammer equation, Ann. Inst. Fourier 44 (1994), 767-810.
32. On contiguity relations of the confluent hypergeometric systems (with Hironobu Kimura and Kyoichi Takano), Proc. Japan Acad. 70, Ser. A (1994), 47-49.
33. On confluences of the general hypergeometric systems (with Hironobu Kimura and Kyoichi Takano), Proc. Japan Acad. 69, Ser. A (1993), 99-104.
34. Contiguity relations of generalized confluent hypergeometric functions (with Hironobu Kimura), Proc. Japan Acad. 69, Ser. A (1993), 105-110.
35. The generalized confluent hypergeometric functions (with Hironobu Kimura and Kyoichi Takano), Proc. Japan Acad. 68, Ser. A (1992), 290-295.
36. G-primitive extensions for linear ordinary differential equations, Kumamoto J. Math. 3 (1990), 1-9.
37. The Galois theory for linear homogeneous partial differential equations of the first order, Funk. Ekvac. 33 (1990), 79-126.
38. Theorems of Sibuya-Malgrange type for Gevrey functions of several variables, Funk. Ekvac. 32 (1989), 365-388.

I am studying on

• Extension of Katz theory on rigid local systems to holonomic systems
• Asymptotic analysis of irregular holonomic systems
• Construction of rigid local systems and study of their properties
• General confluent hypergeometric functions in universal viewpoint

Organizer

• "Invitation to Mathematics" Extenson Lectures at Kumamoto University (Every summer since1996)
• Seminar on Global Analysis at Kumamoto University
• "Various Aspects of Special Functions" Symposium at Kumamoto University, November 1992.
• "Deformation of differential equations and asymptotic analysis" Symposium at RIMS (Research Institute for Mathematical Sciences), 3-7 June 2002.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 20-22 June 2006.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 8-10 October 2007.
• "Workshop on Accessory Parameters" Symposium at Kumamoto University, 2-24 Feburary 2009.
• "Workshop on Accessory Parameters" Symposium at Tambara Institute of Mathematical Sciences, 18-22 June 2009.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 15-17 March 2010.
• "Workshop on Accessory Parameters" Symposium at Tambara Institute of Mathematical Sciences, 9-13 October 2010.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 17-19 March 2011.
• "Workshop on Accessory Parameters" Symposium at Tambara Institute of Mathematical Sciences, 8-11 October 2011.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 15-17 March 2012.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 15-17 March 2013.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 8-10 March 2014.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 13-15 March 2015.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 22-24 March 2016.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 15-17 March 2017.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 14-16 March 2018.
• "Studies on Accessory Parameters" Symposium at Kumamoto University, 13-15 March 2019.

Curriculum Vitae

Born May 8, 1957, Otaru, Hokkaido, Japan

Education

BS 1981, University of Tokyo

MS 1983, University of Tokyo

DS 1988, University of Tokyo

Employment

1988-1994, Assistant Professor, Graduate School of Science and Technology, Kumamoto University

1994-1997, Associate Professor, College of General Education, Kumamoto University

1997-2002, Associate Professor, Department of Mathematics, Kumamoto University

2003-present, Professor, Department of Mathematics, Kumamoto University