Kyushu University Academic Staff Educational and Research Activities Database
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OCHIAI HIROYUKI Last modified date:2018.06.14

Graduate School
Undergraduate School

Changed into new address on Feb 20, 2014 .
Academic Degree
Ph.D(Math. Sci.)
Country of degree conferring institution (Overseas)
Field of Specialization
Algebraic Analysis
Total Priod of education and research career in the foreign country
Outline Activities
Research interest is Algebraic Analysis, Representation Theory and Special Functions. I give courses on these topics as well as undergraduate linear algebra, complex variables, and differential equations for undergraduate and those for graduate students.
Research Interests
  • Representation theory of real reductive Lie groups
    keyword : Algebraic Analysis
Academic Activities
1. Hiroyuki Ochiai, Ken Anjyo, Mathematical Progress in Expressive Image Synthesis II, Springer-Verlag, Selected papers from the proceeding of MEIS2014.
2. Ken Anjyo, Hiroyuki Ochiai, Mathematical Progress in Expressive Image Synthesis I, Springer-Verlag, 2014.08, Selected papers from the proceeding of MEIS2013.
3. Ken Anjyo, Hiroyuki Ochiai, Mathematical Basics of Motion and Deformation in Computer Graphics, Morgan & Claypool Publishers, doi:10.2200/S00599ED1V01Y201409CGR017, 2014.10, [URL], The unique introduction of the mathematical background to the computer graphics.
1. Ken Anjyo, Hiroyuki Ochiai, Mathematical basics of motion and deformation in computer graphics, Synthesis Lectures on Computer Graphics and Animation,, 6, 3, 1-85, 2015.01, This synthesis lecture presents an intuitive introduction to the mathematics of motion and deformation in computer graphics. Starting with familiar concepts in graphics, such as Euler angles, quaternions, and affine transformations, we illustrate that a mathematical theory behind these concepts enables us to develop the techniques for efficient/effective creation of computer animation. This book, therefore, serves as a good guidepost to mathematics (differential geometry and Lie theory) for students of geometric modeling and animation in computer graphics. Experienced developers and researchers will also benefit from this book, since it gives a comprehensive overview of mathematical approaches that are particularly useful in character modeling, deformation, and animation..
2. Shizuo Kaji, Hiroyuki Ochiai, A concise parametrization of affine transformation, SIAM Journal on Imaging Sciences,, 9, 3, 1355-1373, 2016.09, Good parametrizations of affine transformations are essential to interpolation, deformation, and analysis of shape, motion, and animation. It has been one of the central research topics in computer graphics. However, there is no single perfect method and each one has both advantages and disadvantages. In this paper, we propose a novel parametrization of affine transformations, which is a generalization to or an improvement of existing methods. Our method adds yet another choice to the existing toolbox and shows better performance in some applications. A C++ implementation is available to make our framework ready to use in various applications..
3. Piotr Graczyk, Hideyuki Ishi, Salha Mamane, Hiroyuki Ochiai, On the Letac-Massam Conjecture on cones QAn, Proceedings of the Japan Academy Series A: Mathematical Sciences,, 93, 3, 16-21, 2017.03, We prove, for graphical models for nearest neighbour interactions, a conjecture stated by Letac and Massam in 2007. Our result is important in the analysis of Wishart distributions on cones related to graphical models and in its statistical applications..
4. 落合 啓之, Dominic Lanphier, Howard Skogman, Values of twisted tensor L-functions of automorphic forms over imaginary quadratic fields, Canadian J. Math.,, 66, 5, 1078-1109, 2014.04.
5. 落合 啓之, Non-commutative harmonic oscillators, Symmetries, Integrable Systems and Representations, 2013.05.
6. 落合 啓之, Zunderiya Uuganbayar, A generalized hypergeometric system, J. Math. Sci. Univ. Tokyo, 20, 2, 285-315, 2013.06.
7. 落合 啓之, He Xuhua, Nishiyama Kyo, Oshima Yoshiki, On orbits in double flag varieties for symmetric pairs, Transformation Groups, 18, 4, 1091-1136, 2013.06.
8. Kyo Nishiyama and Hiroyuki Ochiai, Double flag varieties for a symmetric pair and finiteness of orbits, Journal of Lie Theory, 21, 79--99, 2011.01.
9. Nobushige Kurokawa and Hiroyuki Ochiai, Zeta functions and Casimir energies on infinite symmetric groups II, Casimir Force, Casimir operators and Riemann hypothesis, 57--63, de Gruyter, 2010.12.
10. Kentaro Ihara and Hiroyuki Ochiai,, Symmetry on linear relations for multiple zeta values,, Nagoya Mathematical Journal, 189, 49--62, 2008.05.
11. 落合啓之, A special value of the spectral zeta function of
the non-commutative harmonic oscillators, The Ramanujan Journal, {\bf 15} (2008) 31--36, 2008.01.
1. Hiroyuki Ochiai, Making a bridge between Ibukiyama and Kobayashi, 第20回整数論オータムワークショップ, 2017.09.
2. Hiroyuki Ochiai, Zeros of Eulerian polynomials, Various Aspects of Multiple Zeta Functions, 2017.08.
3. Hiroyuki Ochiai, Ken Anjyo and Ayumi Kimura, An Elementary Introduction to Matrix Exponential for CG, SIGGRAPH, 2016.07.
4. Hiroyuki Ochiai, Covariant differential operators and Heckman-Opdam hypergeometric systems, International Conference for Korean Mathematical Society 70th Anniversary,, 2016.10, 保形形式に作用する共変な微分作用素を多変数の場合に超幾何関数を用いて記述した。.
5. Hiroyuki Ochiai, Ken Anjyo, An Introduction to Matrix Exponential for CG, 2016.02.
6. 落合 啓之, Covariant differential operators and Heckman–Opdam hypergeometric systems, Analytic Representation Theory of Lie Groups, 2015.07.
7. 落合 啓之, Computer graphics and mathematics, Computational and Geometric Approaches for Nonlinear Phenomena, 2015.08.
8. Ken Anjyo, Hiroyuki Ochiai, Mathematical basics of motion and deformation in computer graphics, ACM SIGGRAPH, 2014.08, This is a course lecture on mathematical basics to graphics community.
9. OCHIAI HIROYUKI, Double flag variety for a symmetric pair and finiteness of orbits, Representation Theory of Chevalley Groups and Related Topics, 2012.03.
10. OCHIAI HIROYUKI, Positivity of alpha determinant, Geometrci Analysis on Euclidean Homogeneous Spaces, 2012.01.
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13. 12/14 と 12/16 の2コマの連続講演.
14. An algebraic transformation of Gauss hypergeometric function.
15. OCHIAI HIROYUKI, Positivity of an alpha determinant, Analysis, Geometry and Group Representations for Homogeneous Spaces, 2010.11.
16. OCHIAI HIROYUKI, Invariant hyperfunctions on some semisimple symmetric space, International conference on representation theory and harmonic analysis, 2010.06.
Membership in Academic Society
  • Japan Mathematical Society
  • On the study of mathematical models of computer graphics
Educational Activities
I give courses for undergraduate and those for graduate students.