Kyushu University [OCHIAI HIROYUKI (Professor) Institute of Mathematics for Industry, Division of Fundamental mathematics]

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

Research Interests

Representation theory of real reductive Lie groups
keyword : Algebraic Analysis
2009.10～2020.03.

Academic Activities

Books

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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.

Papers

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1.	Yasuaki Hiraoka, Hiroyuki Ochiai, and Tomoyuki Shirai, Zeta functions of periodic cubical lattices and cyclotomic-like polynomials, Advanced Studies in Pure Mathematics, 84, 93-121, 2020.03, Zeta functions of periodic cubical lattices are explicitly derived by computing all the eigenvalues of the adjacency operators and their characteristic polynomials. We introduce cyclotomic-like polynomials to give factorization of the zeta function in terms of them and count the number of orbits of the Galois action associated with each cyclotomic-like polynomial to obtain its further factorization. We also give a necessary and sufficient condition for such a polynomial to be irreducible and discuss its irreducibility from this point of view..
2.	Khongorzul Dorjgotov, Hiroyuki Ochiai, Uuganbayar Zunderiya, Exact solutions to a class of time fractional evolution systems with variable coefficients, Journal of Mathematical Physics, 10.1063/1.5035392, 59, 8, 2018.08, We explicitly give new group invariant solutions to a class of Riemann-Liouville time fractional evolution systems with variable coefficients. These solutions are derived from every element in an optimal system of Lie algebras generated by infinitesimal symmetries of evolution systems in the class. We express the solutions in terms of Mittag-Leffler functions, generalized Wright functions, and Fox H-functions and show that these solutions solve diffusion-wave equations with variable coefficients. These solutions contain previously known solutions as particular cases. Some plots of solutions subject to the order of the fractional derivative are illustrated..
3.	Piotr Graczyk, Hideyuki Ishi, Salha Mamane, Hiroyuki Ochiai, On the Letac-Massam Conjecture on cones Q_An, Proceedings of the Japan Academy Series A: Mathematical Sciences, 10.3792/pjaa.93.16, 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.	Shizuo Kaji, Hiroyuki Ochiai, A concise parametrization of affine transformation, SIAM Journal on Imaging Sciences, 10.1137/16M1056936, 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..
5.	Ken Anjyo, Hiroyuki Ochiai, Mathematical basics of motion and deformation in computer graphics, Synthesis Lectures on Computer Graphics and Animation, 10.2200/S00599ED1V01Y201409CGR017, 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..
6.	落合啓之, Dominic Lanphier, Howard Skogman, Values of twisted tensor L-functions of automorphic forms over imaginary quadratic fields, Canadian J. Math., http://dx.doi.org/10.4153/CJM-2013-047-5, 66, 5, 1078-1109, 2014.04.
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.	落合啓之, Zunderiya Uuganbayar, A generalized hypergeometric system, J. Math. Sci. Univ. Tokyo, 20, 2, 285-315, 2013.06.
9.	落合啓之, Non-commutative harmonic oscillators, Symmetries, Integrable Systems and Representations, 2013.05.
10.	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.
11.	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.
12.	Kentaro Ihara and Hiroyuki Ochiai,, Symmetry on linear relations for multiple zeta values,, Nagoya Mathematical Journal, 189, 49--62, 2008.05.
13.	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.

Presentations

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1.	Hiroyuki Ochiai, An absolute version of Hasse zeta functions, Riemann-Roch in characteristic one and related topics, 2019.10.
2.	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.
3.	Hiroyuki Ochiai, Zeros of Eulerian polynomials, Various Aspects of Multiple Zeta Functions, 2017.08.
4.	Hiroyuki Ochiai, Ken Anjyo and Ayumi Kimura, An Elementary Introduction to Matrix Exponential for CG, SIGGRAPH, 2016.07.
5.	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。.
6.	Hiroyuki Ochiai, Ken Anjyo, An Introduction to Matrix Exponential for CG, 2016.02.
7.	落合啓之, Covariant differential operators and Heckman–Opdam hypergeometric systems, Analytic Representation Theory of Lie Groups, 2015.07.
8.	落合啓之, Computer graphics and mathematics, Computational and Geometric Approaches for Nonlinear Phenomena, 2015.08.
9.	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.
10.	OCHIAI HIROYUKI, Double flag variety for a symmetric pair and finiteness of orbits, Representation Theory of Chevalley Groups and Related Topics, 2012.03.
11.	OCHIAI HIROYUKI, Positivity of alpha determinant, Geometrci Analysis on Euclidean Homogeneous Spaces, 2012.01.
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14.	12/14 と 12/16 の２コマの連続講演.
15.	An algebraic transformation of Gauss hypergeometric function.
16.	OCHIAI HIROYUKI, Positivity of an alpha determinant, Analysis, Geometry and Group Representations for Homogeneous Spaces, 2010.11.
17.	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

Awards

On the study of mathematical models of computer graphics

Educational

Educational Activities

I give courses for undergraduate and those for graduate students.

Social

Professional and Outreach Activities

I got Award as a Reviewer for JSPS grant..

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website for research, education of Hiroyuki Ochiai .