Updated on 2025/04/01

Information

 

写真a

 
OCHIAI HIROYUKI
 
Organization
Institute of Mathematics for Industry Division of Fundamental mathematics Professor
School of Sciences Department of Mathematics(Concurrent)
Graduate School of Mathematics Department of Mathematics(Concurrent)
Joint Graduate School of Mathematics for Innovation (Concurrent)
Title
Professor
Profile
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.
Homepage
External link

Research Areas

  • Natural Science / Basic analysis

Degree

  • Ph.D(Math. Sci.)

Research History

  • 九州大学 マス・フォア・インダストリ研究所 教授   

    2011.4 - Present

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  • 立教大学1989.4-1998.3. 東京工業大学2001.4-2002.9. 名古屋大学2002.10-2009.3.   

Research Interests・Research Keywords

  • Research theme: 表現論

    Keyword: 表現論

    Research period: 2025

  • Research theme: Representation Theory

    Keyword: Representation Theory

    Research period: 2024

  • Research theme: 代数解析学

    Keyword: 代数解析学

    Research period: 2024

  • Research theme: Algebraic Analysis

    Keyword: Algebraic Analysis

    Research period: 2024

  • Research theme: Representation theory of real reductive Lie groups

    Keyword: Algebraic Analysis

    Research period: 2009.10 - 2033.3

Awards

  • 平成26年度科学技術分野の文部科学大臣表彰科学技術賞(研究部門)

    2014.4   文部科学省   On the study of mathematical models of computer graphics

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    受賞題目は、「CG映像制作のための演出技術の数理モデルに関する研究」と題するもので、安生健一氏(OLMデジタル)ならびに土橋宣典氏(北海道大学)との共同受賞です。受賞対象となった研究は、CG を用いた映像制作においてアニメータなどの作成者の利便性向上のための数理モデルの構築を行ったものです。CG分野と数学分野の研究者が産業界と協働することによって実現しました。本研究では、3次元CGにおいて最も重要かつ困難な表示対象である流体とキャラクター(人間や動物など)を対象とし、映像の作り手の意図を直接的・直感的に指示するための新しい数理モデルを構築しました。

Papers

  • Exact Convergence Rates of Alternating Projections for Nontransversal Intersections Invited Reviewed International journal

    Hiroyuki Ochiai, Yoshiyuki Sekiguchi, Hayato Waki,

    Japan Journal of Industrial and Applied Mathematics   41   57 - 83   2024.4

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Exact convergence rates of alternating projections for nontransversal intersections Invited Reviewed International journal

    Hiroyuki Ochiai, Yoshiyuki Sekiguchi, Hayato Waki

    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS   41 ( 1 )   57 - 83   2023.4   ISSN:0916-7005 eISSN:1868-937X

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Japan Journal of Industrial and Applied Mathematics  

    We consider the convergence rate of the alternating projection method for the nontransversal intersection of a semialgebraic set and a linear subspace. For such an intersection, the convergence rate is known as sublinear in the worst case. We study the exact convergence rate for a given semialgebraic set and an initial point, and investigate when the convergence rate is linear or sublinear. As a consequence, we show that the exact rates are expressed by multiplicities of the defining polynomials of the semialgebraic set, or related power series in the case that the linear subspace is a line, and we also decide the convergence rate for given data by using elimination theory. Our methods are also applied to give upper bounds for the case that the linear subspace has the dimension more than one. The upper bounds are shown to be tight by obtaining exact convergence rates for a specific semialgebraic set, which depend on the initial points.

    DOI: 10.1007/s13160-023-00584-9

    Web of Science

    Scopus

  • A study of a Fuchsian system of rank 8 in 3 variables and the ordinary differential equations as its restrictions, Reviewed International journal

    Akihito Ebisu, Yoshishige Haraoka, Masanobu Kaneko, Hiroyuki Ochiai, Takeshi Sasaki and Masaaki Yoshida

    Osaka Math. J.   60   151 - 204   2023.4

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Comments on efficient batch verification test for digital signatures based on elliptic curves Invited Reviewed International journal

    Keisuke Hakuta, Hiroyuki Ochiai, Tsuyoshi Takagi

    MATHEMATICA SLOVACA   72 ( 3 )   575 - 590   2022.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1515/ms-2022-0038

  • Method of the fundamental solution for the Neumann problems of the modified Helmholtz equation in disk domain Reviewed International journal

    Shin-Ichiro Ei, Hiroyuki Ochiai, and Yoshitaro Tanaka

    Journal of Computational and Applied Mathematics   402   2022.3   ISSN:0377-0427 eISSN:1879-1778

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Journal of Computational and Applied Mathematics  

    The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the domain and determining the coefficients of the linear sum to satisfy the boundary condition on the finite points of the boundary. In this paper, the existence of the approximate solution by the MFS for the Neumann problems of the modified Helmholtz equation in disk domains is rigorously demonstrated. We reveal the sufficient condition of the existence of the approximate solution. Applying the Green formula to the Neumann problem of the modified Helmholtz equation, we bound the error between the approximate solution and exact solution into the difference of the function of the boundary condition and the normal derivative of the approximate solution by boundary integrations. Using this estimate of the error, we show the convergence of the approximate solution by the MFS to the exact solution with exponential order, that is, N2aN order, where a is a positive constant less than one and N is the number of collocation points. Furthermore, it is demonstrated that the error tends to 0 in exponential order in the numerical simulations with increasing number of collocation points N.

    DOI: 10.1016/j.cam.2021.113795

    Web of Science

    Scopus

    Other Link: https://www.sciencedirect.com/science/article/pii/S0377042721004179?via%3Dihub

  • Comments on efficient batch verification test for digital signatures based on elliptic curves Invited Reviewed International journal

    KEISUKE HAKUTA, HIROYUKI OCHIAI, AND TSUYOSHI TAKAGI

    Mathematica Slovaca   72 ( 3 )   575 - 590   2022.3

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

    Batch verification for digital signature scheme is a method to verify multiple signatures
    simultaneously. The complex exponent test (CE test for short) proposed by Cheon and Lee is one of
    the most efficient batch verification tests for several digital signature schemes on certain types of elliptic
    curves (including Koblitz curves). The security of the CE test relies essentially on the cardinality of
    a subset of a residue ring of the endomorphism ring of an elliptic curve over an ideal. They have
    evaluated the cardinality of the above subset, and have illustrated the effectiveness of the CE test by
    using the evaluation. The aim of this paper is to point out that their evaluation contains a flaw. The
    flaw is generally related to two roots of a quadratic equation which is used in their argument. We
    mend the flaw of their evaluation. Our correct evaluation shows that the CE test can achieve the same
    security as the underlying signature scheme on Koblitz curves. As a result, the CE test is a secure
    batch verification when the underlying signature scheme uses Koblitz curves.

    DOI: 10.1515/ms-2022-0038

  • Symmetry of Dressed Photon Reviewed International journal

    Hiroyuki Ochiai

    Symmetry   13 ( 7 )   1283   2021.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    Motivated by describing the symmetry of a theoretical model of dressed photons, we introduce several spaces with Lie group actions and the morphisms between them depending on three integer parameters n≥r≥s on dimensions. We discuss the symmetry on these spaces using classical invariant theory, orbit decomposition of prehomogeneous vector spaces, and compact reductive homogeneous space such as Grassmann manifold and flag variety. Finally, we go back to the original dressed photon with n=4,r=2,s=1

    DOI: https://doi.org/10.3390/sym13071283

    Other Link: https://www.mdpi.com/2073-8994/13/7/1283

  • Zeta functions of periodic cubical lattices and cyclotomic-like polynomials Invited Reviewed International journal

    Yasuaki Hiraoka, Hiroyuki Ochiai, and Tomoyuki Shirai

    Advanced Studies in Pure Mathematics   84   93 - 121   2020.4

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    Language:English   Publishing type:Research paper (scientific journal)  

    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.

  • Exact solutions to a class of time fractional evolution systems with variable coefficients Reviewed International journal

    Khongorzul Dorjgotov, Hiroyuki Ochiai, Uuganbayar Zunderiya

    Journal of Mathematical Physics   59 ( 8 )   2018.8

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    Language:English   Publishing type:Research paper (scientific journal)  

    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.

    DOI: 10.1063/1.5035392

  • On the Letac-Massam Conjecture on cones QAn Reviewed

    Piotr Graczyk, Hideyuki Ishi, Salha Mamane, Hiroyuki Ochiai

    Proceedings of the Japan Academy Series A: Mathematical Sciences   93 ( 3 )   16 - 21   2017.3

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    Language:English   Publishing type:Research paper (scientific journal)  

    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.

    DOI: 10.3792/pjaa.93.16

  • A concise parametrization of affine transformation Reviewed International journal

    Shizuo Kaji, Hiroyuki Ochiai

    SIAM Journal on Imaging Sciences   9 ( 3 )   1355 - 1373   2016.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    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.

    DOI: 10.1137/16M1056936

  • Mathematical basics of motion and deformation in computer graphics Reviewed

    Ken Anjyo, Hiroyuki Ochiai

    Synthesis Lectures on Computer Graphics and Animation   6 ( 3 )   1 - 85   2015.1

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    Language:English   Publishing type:Research paper (scientific journal)  

    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.

    DOI: 10.2200/S00599ED1V01Y201409CGR017

  • Values of twisted tensor L-functions of automorphic forms over imaginary quadratic fields Reviewed International journal

    落合 啓之, Dominic Lanphier, Howard Skogman

    Canadian J. Math.   66 ( 5 )   1078 - 1109   2014.4

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: http://dx.doi.org/10.4153/CJM-2013-047-5

  • On orbits in double flag varieties for symmetric pairs Reviewed International journal

    落合 啓之, He Xuhua, Nishiyama Kyo, Oshima Yoshiki

    Transformation Groups   18 ( 4 )   1091 - 1136   2013.6

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    Language:English   Publishing type:Research paper (scientific journal)  

  • A generalized hypergeometric system Reviewed

    落合 啓之, Zunderiya Uuganbayar

    J. Math. Sci. Univ. Tokyo   20 ( 2 )   285 - 315   2013.6

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    Language:English   Publishing type:Research paper (bulletin of university, research institution)  

  • Non-commutative harmonic oscillators Invited Reviewed International journal

    落合 啓之

    Symmetries, Integrable Systems and Representations   2013.5

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    Language:English   Publishing type:Research paper (international conference proceedings)  

  • Double flag varieties for a symmetric pair and finiteness of orbits Reviewed International journal

    Kyo Nishiyama and Hiroyuki Ochiai

    Journal of Lie Theory   21   2011.1

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Zeta functions and Casimir energies on infinite symmetric groups II Invited Reviewed International journal

    Nobushige Kurokawa and Hiroyuki Ochiai

    Casimir Force, Casimir operators and Riemann hypothesis   2010.12

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    Language:English   Publishing type:Research paper (international conference proceedings)  

  • Symmetry on linear relations for multiple zeta values, Reviewed

    Kentaro Ihara and Hiroyuki Ochiai,

    Nagoya Mathematical Journal   189   2008.5

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    Language:English   Publishing type:Research paper (bulletin of university, research institution)  

  • A special value of the spectral zeta function of the non-commutative harmonic oscillators Reviewed International journal

    落合啓之

    The Ramanujan Journal   2008.1

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    Language:English   Publishing type:Research paper (scientific journal)  

    A special value of the spectral zeta function of the non-commutative harmonic oscillators

  • Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs: II. Dynamical correspondence

    Kodani, H; Matsue, K; Ochiai, H; Takayasu, A

    NONLINEARITY   38 ( 4 )   2025.4   ISSN:0951-7715 eISSN:1361-6544

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    Publisher:Nonlinearity  

    In this paper, we provide a natural correspondence of eigenstructures of Jacobian matrices associated with equilibria for appropriately transformed two systems describing finite-time blow-ups for ODEs with quasi-homogeneity in an asymptotic sense. As a corollary, we see that asymptotic expansions of blow-ups proposed in Part I themselves provide a criterion of the existence of blow-ups with an intrinsic gap structure of stability information among two systems. Examples provided in Part I are revisited to show the above correspondence.

    DOI: 10.1088/1361-6544/adb52e

    Web of Science

    Scopus

  • Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs: I. Method and justification

    Asai, T; Kodani, H; Matsue, K; Ochiai, H; Sasaki, T

    NONLINEARITY   38 ( 4 )   2025.4   ISSN:0951-7715 eISSN:1361-6544

  • Analytic formulas for alternating projection sequences for the positive semidefinite cone and an application to convergence analysis

    Ochiai H., Sekiguchi Y., Waki H.

    Journal of Mathematical Analysis and Applications   544 ( 1 )   2025.4   ISSN:0022247X eISSN:1096-0813

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    Publisher:Journal of Mathematical Analysis and Applications  

    We derive analytic formulas for the alternating projection method applied to the cone S+n of positive semidefinite matrices and an affine subspace. More precisely, we find recursive relations on parameters representing a sequence constructed by the alternating projection method. By applying these formulas, we analyze the alternating projection method in detail and show that the upper bound given by the singularity degree is actually tight when the alternating projection method is applied to S+3 and a 3-plane whose intersection is a singleton with singularity degree 2.

    DOI: 10.1016/j.jmaa.2024.129070

    Web of Science

    Scopus

  • A D-module approach to invariant distributions with finitely many orbits

    Ochiai H.

    Indagationes Mathematicae   36 ( 2 )   497 - 506   2024   ISSN:00193577 eISSN:1872-6100

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    Publisher:Indagationes Mathematicae  

    Tauchi provides an example illustrating the action of a real algebraic subgroup H of GL(2n,R) with finitely many orbits on R2n, while the dimension of the space of relative H-invariant distributions on R2n is infinite. We offer a perspective on this example from the viewpoint of D-modules, where we explicitly determine the simple quotient regular holonomic D-modules and demonstrate that the distributions exhibit an enlarged symmetry.

    DOI: 10.1016/j.indag.2024.07.006

    Web of Science

    Scopus

  • A STUDY OF A FUCHSIAN SYSTEM OF RANK 8 IN 3 VARIABLES AND THE ORDINARY DIFFERENTIAL EQUATIONS AS ITS RESTRICTIONS (vol 60, pg 153, 2023)

    Ebisu, A; Haraoka, Y; Kaneko, M; Ochiai, H; Sasaki, T; Yoshida, M

    OSAKA JOURNAL OF MATHEMATICS   60 ( 2 )   491 - 492   2023.4   ISSN:0030-6126

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  • A STUDY OF A FUCHSIAN SYSTEM OF RANK 8 IN 3 VARIABLES AND THE ORDINARY DIFFERENTIAL EQUATIONS AS ITS RESTRICTIONS

    Ebisu A., Haraoka Y., Kaneko M., Ochiai H., Sasaki T., Yoshida M.

    Osaka Journal of Mathematics   60 ( 1 )   153 - 206   2023.1   ISSN:00306126

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    Publisher:Osaka Journal of Mathematics  

    A Fuchsian system of rank 8 in 3 variables with 4 parameters is found. The singular locus consists of six planes and a cubic surface. The restriction of the system onto the intersection of two singular planes is an ordinary differential equation of order four with three singular points. A middle convolution of this equation turns out to be the tensor product of two Gauss hypergeometric equations, and another middle convolution sends this equation to the Dotsenko-Fateev equation. Local solutions of these ordinary differential equations are found. Their coefficients are sums of products of the Gamma functions. These sums can be expressed as special values of the generalized hypergeometric series4 F3 at 1.

    Scopus

  • Off-Shell Quantum Fields to Connect Dressed Photons with Cosmology Reviewed International journal

    Hirofumi Sakuma, Izumi Ojima, Motoichi Ohtsu and Hiroyuki Ochiai

    Symmetry   12 ( 8 )   1244   2020.8

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    Language:Japanese   Publishing type:Research paper (scientific journal)  

    DOI: https://doi.org/10.3390/sym12081244

  • On solutions of linear fractional differential equations and systems thereof Reviewed

    Khongorzul Dorjgotov, Hiroyuki Ochiai, Uuganbayar Zunderiya

    Fractional Calculus and Applied Analysis   22 ( 2 )   479 - 494   2019.4

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    Language:English   Publishing type:Research paper (scientific journal)  

    We derive exact solutions to classes of linear fractional differential equations and systems thereof expressed in terms of generalized Wright functions and Fox H-functions. These solutions are invariant solutions of diffusion-wave equations obtained through certain transformations, which are briefly discussed. We show that the solutions given in this work contain previously known results as particular cases.

    DOI: 10.1515/fca-2019-0028

  • Lie symmetry analysis of a class of time fractional nonlinear evolution systems Reviewed

    Khongorzul Dorjgotov, Hiroyuki Ochiai, Uuganbayar Zunderiya

    Applied Mathematics and Computation   329   105 - 117   2018.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    We study a class of nonlinear evolution systems of time fractional partial differential equations using Lie symmetry analysis. We obtain not only infinitesimal symmetries but also a complete group classification and a classification of group invariant solutions of this class of systems. We find that the class of systems of differential equations studied is naturally divided into two cases on the basis of the type of a function that they contain. In each case, the dimension of the Lie algebra generated by the infinitesimal symmetries is greater than 2, and for this reason we present the structures and one-dimensional optimal systems of these Lie algebras. The reduced systems corresponding to the optimal systems are also obtained. Explicit group invariant solutions are found for particular cases.

    DOI: 10.1016/j.amc.2018.01.056

  • An elementary introduction to matrix exponential for CG

    Hiroyuki Ochiai, Ken Anjyo, Ayumi Kimura

    ACM International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2016 ACM SIGGRAPH 2016 Courses, SIGGRAPH 2016   2016.7

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    Language:English   Publishing type:Research paper (other academic)  

    DOI: 10.1145/2897826.2927338

  • Zeta Functions of Representations

    Nobushige Kurokawa, Hiroyuki Ochiai

    Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi   63 ( 1 )   215 - 222   2014.12

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    Language:English  

    Zeta Functions of Representations

    DOI: 10.14992/00010884

  • Values of Twisted Tensor L-functions of Automorphic Forms Over Imaginary Quadratic Fields Reviewed

    Dominic Lanphier, Howard Skogman, Hiroyuki Ochiai

    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES   66 ( 5 )   1078 - 1109   2014.10

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    Language:English   Publishing type:Research paper (scientific journal)  

    Let K be a complex quadratic extension of Q and let A(K) denote the adeles of K. We find special values at all of the critical points of twisted tensor L-functions attached to cohomological cuspforms on GL(2)(AK) and establish Galois equivariance of the values. To investigate the values, we determine the archimedean factors of a class of integral representations of these L-functions, thus proving a conjecture due to Ghate. We also investigate analytic properties of these L-functions, such as their functional equations.

    DOI: 10.4153/CJM-2013-047-5

  • Closed orbits on partial flag varieties and double flag variety of finite type Reviewed

    Keisuke Kondo, Kyo Nishiyama, Hiroyuki Ochiai, Kenji Taniguchi

    Kyushu J. Math.   68 ( 1 )   113 - 119   2014.4

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Closed orbits on partial flag varieties and double flag variety of finite type Reviewed

    Kensuke Kondo, Kyo Nishiyama, Hiroyuki Ochiai, Kenji Taniguchi

    Kyushu Journal of Mathematics   68 ( 1 )   113 - 119   2014.1

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    Let G be a connected reductive algebraic group over C. We denote by K = (Gθ)0the identity component of the fixed points of an involutive automorphism θ of G. The pair (G, K) is called a symmetric pair. Let Q be a parabolic subgroup of K. We want to find a pair of parabolic subgroups P 1, P 2of G such that (i) P 1∩ P 2= Q and (ii) P 1 P 2is dense in G. The main result of this article states that, for a simple group G, we can find such a pair if and only if (G, K) is a Hermitian symmetric pair. The conditions (i) and (ii) imply that the K -orbit through the origin (eP 1, eP 2) of G/P 1× G/P 2is closed and it generates an open dense G -orbit on the product of partial flag variety. From this point of view, we also give a complete classification of closed K -orbits on G/P 1× G/P 2.

    DOI: 10.2206/kyushujm.68.113

  • Mathematical basics of motion and deformation in computer graphics

    Ken Anjyo, Hiroyuki Ochiai

    Mathematical Basics of Motion and Deformation in Computer Graphics   1 - 82   2014.1

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    Language:English  

    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.

  • Mathematical basics of motion and deformation in computer graphics

    Hiroyuki Ochiai, Ken Anjyo

    ACM Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2014 ACM SIGGRAPH 2014 Courses, SIGGRAPH 2014   2014.1

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    Language:English   Publishing type:Research paper (other academic)  

    DOI: 10.1145/2614028.2615386

  • Generating various flow fields using principal component analysis

    Syuhei Sato, Yoshinori Dobashi, Kei Iwasaki, Hiroyuki Ochiai, Tsuyoshi Yamamoto, Tomoyuki Nishita

    ACM Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2014 ACM SIGGRAPH 2014 Posters, SIGGRAPH 2014   2014

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    Language:English   Publishing type:Research paper (other academic)  

    DOI: 10.1145/2614217.2630575

  • Mathematical description of motion and deformation - From basics to graphics applications

    Hiroyuki Ochiai, Ken Anjyo

    SIGGRAPH Asia 2013 Courses, SA 2013 SIGGRAPH Asia 2013 Courses, SA 2013   2013.12

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    Language:English   Publishing type:Research paper (other academic)  

    While many technical terms, such as Euler angle, quaternion, and affine transformation, now become quite popular in computer graphics, their graphical meanings are sometimes a bit far from the original mathematical entities, which might cause misunderstanding or misuse of the mathematical techniques. This course presents an intuitive introduction to several mathematical concepts that are quite useful for describing motion and deformation of geometric objects. The concepts are inherited mostly from differential geometry and Lie theory, and now commonly used in various aspects of computer graphics, including curve/surface editing, deformation and animation of geometric objects. The objective of this course is to fill the gap between the original mathematical concepts and the practical meanings in computer graphics without assuming any prior knowledge of pure mathematics. We then illustrate practical usefulness of deep understanding of the mathematical concepts. Moreover this course demonstrates our current/ongoing research work, which is benefited from our mathematical formulation.

    DOI: 10.1145/2542266.2542268

  • On Orbits in Double Flag Varieties for Symmetric Pairs Reviewed

    Xuhua He, Hiroyuki Ochiai, Kyo Nishiyama, Yoshiki Oshima

    Transformation Groups   18 ( 4 )   1091 - 1136   2013.12

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    Let G be a connected, simply connected semisimple algebraic group over the complex number field, and let K be the fixed point subgroup of an involutive automorphism of G so that (G, K) is a symmetric pair. We take parabolic subgroups P of G and Q of K, respectively, and consider the product of partial flag varieties G/P and K/Q with diagonal K-action, which we call a double flag variety for a symmetric pair. It is said to be of finite type if there are only finitely many K-orbits on it. In this paper, we give a parametrization of K-orbits on G/P × K/Q in terms of quotient spaces of unipotent groups without assuming the finiteness of orbits. If one of P ⊂ G or Q ⊂ K is a Borel subgroup, the finiteness of orbits is closely related to spherical actions. In such cases, we give a complete classification of double flag varieties of finite type, namely, we obtain classifications of K-spherical flag varieties G/P and G-spherical homogeneous spaces G/Q.

    DOI: 10.1007/s00031-013-9243-8

  • ZEROS OF WITTEN ZETA FUNCTIONS AND ABSOLUTE LIMIT Reviewed

    Nobushige Kurokawa, Hiroyuki Ochiai

    KODAI MATHEMATICAL JOURNAL   36 ( 3 )   440 - 454   2013.10

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  • Dualities for absolute zeta functions and multiple gamma functions Reviewed

    Nobushige Kurokawa, Hiroyuki Ochiai

    Proceedings of the Japan Academy Series A: Mathematical Sciences   89 ( 7 )   75 - 79   2013.7

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    We study absolute zeta functions from the view point of a canonical normalization. We introduce the absolute Hurwitz zeta function for the normalization. In particular, we show that the theory of multiple gamma and sine functions gives good normalizations in cases related to the Kurokawa tensor product. In these cases, the functional equation of the absolute zeta function turns out to be equivalent to the simplicity of the associated non-classical multiple sine function of negative degree.

    DOI: 10.3792/pjaa.89.75

  • A generalized hypergeometric system Reviewed

    Hiroyuki Ochiai, Uuganbayar Zunderiya

    Journal of Mathematical Sciences (Japan)   20 ( 2 )   285 - 315   2013

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    We give a combinatorial formula of the dimension of global solutions to a generalization of Gauss-Aomoto-Gelfand hypergeometric system, where the quadratic differential operators are replaced by higher order operators. We also derive a polynomial estimate of the dimension of global solutions for the case in 3 × 3 variables.

  • Zeros of Witten zeta functions and absolute limit Reviewed

    Nobushige Kurokawa, Hiroyuki Ochiai

    Kodai Mathematical Journal   36 ( 3 )   440 - 454   2013

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    DOI: 10.2996/kmj/1383660691

  • Non-commutative harmonic oscillators

    Hiroyuki Ochiai

    Symmetries, Integrable Systems and Representations   40   483 - 490   2013

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    This is a survey on the non-commutative harmonic oscillator, which is a generalization of usual (scalar) harmonic oscillators to the system introduced by Parmeggiani and Wakayama.With the definitions and the basic properties, we summarize the positivity of several related operators with sl
    2 interpretations. We also mention some unsolved questions, in order to clarify the current status of the problems and expected further development.

    DOI: 10.1007/978-1-4471-4863-0_19

  • Generating flow fields variations by modulating amplitude and resizing simulation space

    Syuhei Sato, Yoshinori Dobashi, Kei Iwasaki, Hiroyuki Ochiai, Tsuyoshi Yamamoto

    SIGGRAPH Asia 2013 Technical Briefs, SA 2013 SIGGRAPH Asia 2013 Technical Briefs, SA 2013   2013

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    The visual simulation of fluids has become an important element in many applications, such as movies and computer games. In these applications, large-scale fluid scenes, such as fire in a village, are often simulated by repeatedly rendering multiple small-scale fluid flows. In these cases, animators are requested to generate many variations of a small-scale fluid flow. This paper presents a method to help animators meet such requirements. Our method enables the user to generate flow field variations from a single simulated dataset obtained by fluid simulation. The variations are generated in both the frequency and spatial domains. Fluid velocity fields are represented using Laplacian eigenfunctions which ensure that the flow field is always incompressible. In generating the variations in the frequency domain, we modulate the coefficients (amplitudes) of the basis functions. To generate variations in the spatial domain, our system expands or contracts the simulation space, then the flow is calculated by solving a minimization problem subject to the resized velocity field. Using our method, the user can easily create various animations from a single dataset calculated by fluid simulation. 2013 Copyright held by the Owner/Author.

    DOI: 10.1145/2542355.2542371

  • Holonomic systems of Gegenbauer type polynomials of matrix arguments related with Siegel modular forms Reviewed

    Tomoyoshi Ibukiyama, Takako Kuzumaki, Hiroyuki Ochiai

    Journal of the Mathematical Society of Japan   64 ( 1 )   273 - 316   2012.10

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    Differential operators on Siegel modular forms which behave well under the restriction of the domain are essentially intertwining operators of the tensor product of holomorphic discrete series to its irreducible components. These are characterized by polynomials in the tensor of pluriharmonic polynomials with some invariance properties. We give a concrete study of such polynomials in the case of the restriction from Siegel upper half space of degree 2n to the product of degree n. These generalize the Gegenbauer polynomials which appear for n = 1. We also describe their radial parts parametrization and differential equations which they satisfy, and show that these differential equations give holonomic systems of rank 2 n.

    DOI: 10.2969/jmsj/06410273

  • Holonomic system of Gegenbauer type polynomials Reviewed

    Tomoyoshi Ibukiyama, Takako Kuzumaki, Hiroyuki Ochiai

    Journal of Mathematical Society of Japan   64 ( 1 )   2012.1

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  • Holonomic systems of Gegenbauer type polynomials of matrix arguments related with Siegel modular forms Reviewed

    Tomoyoshi Ibukiyama, Takako Kuzumaki, Hiroyuki Ochiai

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   64 ( 1 )   273 - 316   2012.1

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    Differential operators on Siegel modular forms which behave well under the restriction of the domain are essentially intertwining operators of the tensor product of holomorphic discrete series to its irreducible components. These are characterized by polynomials in the tensor of pluriharmonic polynomials with some invariance properties. We give a concrete study of such polynomials in the case of the restriction from Siegel upper half space of degree 2n to the product of degree n. These generalize the Gegenbauer polynomials which appear for n = 1. We also describe their radial parts parametrization and differential equations which they satisfy, and show that these differential equations give holonomic systems of rank 2(n).

    DOI: 10.2969/jmsj/06410273

  • A multivariable Euler product of Igusa type and its applications Reviewed

    Nobushige Kurokawa, Hiroyuki Ochiai

    Journal of Number Theory   129 ( 8 )   1919 - 1930   2009.8

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    Knowing the number of solutions for a Diophantine equation is an important step to study various arithmetic problems. Igusa originated the study of Igusa zeta functions associated to local Diophantine problems. Multiplying all these local Igusa zeta functions we obtain the global version in the natural way. Unfortunately, investigations on global Igusa zeta functions are rare up to now. Reformulating the global Igusa zeta function via the number of morphisms between algebraic systems we discover a new aspect: the multivariable Euler product of Igusa type and its applications. A purpose of this paper is to encourage experts for further studies on global Igusa zeta functions by treating a simple interesting example.

    DOI: 10.1016/j.jnt.2008.10.008

  • Spectra of alternating Hilbert operators, Invited Reviewed International journal

    Nobushige Kurokawa and Hiroyuki Ochiai,

    Spectral Analysis in Geometry and Number Theory, Contemporary Mathematics   484   2009.5

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  • On value-relations, functional relations and singularities of Mordell-Tornheim and related triple zeta-functions Reviewed

    Kohji Matsumoto, Takashi Nakamura, Hiroyuki Ochiai, Hirofumi Tsumura

    Acta Arithmetica   132 ( 2 )   99 - 125   2008.8

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    DOI: 10.4064/aa132-2-1

  • Higher Mahler measures and zeta functions, Reviewed International journal

    Nobushige Kurokawa, Matilde Lalin and Hiroyuki Ochiai,

    Acta Arithmetica   135   2008.5

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  • A special value of the spectral zeta function of the non-commutative harmonic oscillators Reviewed

    Hiroyuki Ochiai

    Ramanujan Journal   15 ( 1 )   31 - 36   2008.1

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    The non-commutative harmonic oscillator is a 2×2-system of harmonic oscillators with a non-trivial correlation. We write down explicitly the special value at s=2 of the spectral zeta function of the non-commutative harmonic oscillator in terms of the complete elliptic integral of the first kind, which is a special case of a hypergeometric function.

    DOI: 10.1007/s11139-007-9065-1

  • Higher Mahler measures and zeta functions Reviewed

    N. Kurokawa, M. Lalín, Hiroyuki Ochiai

    Acta Arithmetica   135 ( 3 )   269 - 297   2008

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    DOI: 10.4064/aa135-3-5

  • Symmetry on linear relations for multiple zeta values Reviewed

    Kentaro Ihara, Hiroyuki Ochiai

    Nagoya Mathematical Journal   189   49 - 62   2008

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    We find a symmetry for the reflection groups in the double shuffle space of depth three. The space was introduced by Ihara, Kaneko and Zagier and consists of polynomials in three variables satisfying certain identities which are connected with the double shuffle relations for multiple zeta values. Goncharov has defined a space essentially equivalent to the double shuffle space and has calculated the dimension. In this paper we relate the structure among multiple zeta values of depth three with the invariant theory for the reflection groups and discuss the dimension of the double shuffle space in this view point.

  • An expression of harmonic vector fields on hyperbolic 3-cone-manifolds in terms of hypergeometric functions Reviewed

    Michihiko Fujii, Hiroyuki Ochiai

    Publications of the Research Institute for Mathematical Sciences   43 ( 3 )   727 - 761   2007.9

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    Let V be a neighborhood of a singular locus of a hyperbolic 3-cone-manifold, which is a quotient space of the 3-dimensional hyperbolic space. In this paper we give an explicit expression of a harmonic vector field v on the hyperbolic manifold V in terms of hypergeometric functions. The expression is obtained by solving a system of ordinary differential equations which is induced by separation of the variables in the vector-valued partial differential equation (Δ + 4)τ = 0, where Δ is the Laplacian of V and τ is the dual 1-form of v. We transform this system of ordinary differential equations to single-component differential equations by elimination of unknown functions and solve these equations. The most important step in solving them consists of two parts, decomposing their differential operators into differential operators of the type appearing in Riemann's P-equation in the ring of differential operators and then describing the projections to the components of this decomposition in terms of differential operators that are also of the type appearing in Riemann's P-equation.

    DOI: 10.2977/prims/1201012040

  • An expression of harmonic vector fields on hyperbolic 3-cone-manifolds in terms of hypergeometric functions Reviewed

    Michihiko Fujii, Hiroyuki Ochiai

    PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES   43 ( 3 )   727 - 761   2007.9

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    Lot V be a neighborhood of a singular locus of a hyperbolic 3-cone-manifold, which is a quotient space of the 3-dimensional hyperbolic space. In this paper we give an explicit expression of a harmonic vector field v on the hyperbolic manifold V in terms of hypergeometric functions. The expression is obtained by solving a system of ordinary differential equations which is induced by separation of the variables in the vector-valued partial differential equation (A + 4)tau = 0, where Delta is the Laplacian of V and tau is the dual 1-form of v. We transform this system of ordinary differential equations to single-component differential equations by elimination of unknown functions and solve these equations. The most important step in solving them consists of two parts, decomposing their differential operators into differential operators of the type appearing in Riemann's P-equation in the ring of differential operators and then describing the projections to the components of this decomposition in terms of differential operators that are also of the type appearing in Riemann's P-equation.

    DOI: 10.2977/prims/1201012040

  • Generalized Kinkelin's formulas Reviewed

    Nobushige Kurokawa, Hiroyuki Ochiai

    KODAI MATHEMATICAL JOURNAL   30 ( 2 )   195 - 212   2007.6

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    DOI: 10.2996/kmj/1183475511

  • Arithmetic structure of CMSZ fake projective planes Reviewed

    Fumiharu Kato, Hiroyuki Ochiai

    Journal of Algebra   305 ( 2 )   1166 - 1185   2006.11

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    We show that the fake projective planes that are constructed from dyadic discrete subgroups discovered by Cartwright, Mantero, Steger, and Zappa are realized as connected components of certain unitary Shimura surfaces. As a corollary we show that these fake projective planes have models defined over the number field Q (sqrt(-3), sqrt(5)).

    DOI: 10.1016/j.jalgebra.2006.07.019

  • Theta lifting of nilpotent orbits for symmetric pairs Reviewed

    Kyo Nishiyama, Hiroyuki Ochiai, Chen Bo Zhu

    Transactions of the American Mathematical Society   358 ( 6 )   2713 - 2734   2006.6

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    We consider a reductive dual pair (G, G′) in the stable range with G′ the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K′-orbits, where K′ is a maximal compact subgroup of G′ and we describe the precise K -module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair (G, K). As an application, we prove sphericality and normality of the closure of certain nilpotent K -orbits obtained in this way. We also give integral formulas for their degrees.

    DOI: 10.1090/S0002-9947-05-03826-2

  • Scaling Limit of Successive Approximations for w′=-w2 Reviewed

    Tetsuya Hattori, Hiroyuki Ochiai

    Funkcialaj Ekvacioj   49 ( 2 )   291 - 319   2006.1

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    We prove existence of scaling limits of sequences of functions defined by the recursion relation w′n+1(ϰ)= -wn(ϰ)2. which is a successive approximation to w′(ϰ)= -wn(ϰ)2 a simplest non-linear ordinary differential equation whose solutions have moving singularities. Namely, the sequence approaches the exact solution as n→ √ in an asymptotically conformal way, [formula omitted], for a sequence of numbers {qn} and a function [formula omitted]. We also discuss implication of the results in terms of random sequential bisections of a rod.

    DOI: 10.1619/fesi.49.291

  • Invariant distributions on a non-isotropic pseudo-Riemannian symmetric space of rank one Reviewed

    Hiroyuki Ochiai

    Indagationes Mathematicae   16 ( 3-4 )   631 - 638   2005.12

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    We investigate the structure of invariant distributions on a non-isotropic non-Riemannian symmetric space of rank one. Especially, the J-criterion related to the generalized Gelfand pair is shown for this space without imposing the condition on the eigenfuction of the Laplace-Bertrami operator.

    DOI: 10.1016/S0019-3577(05)80043-6

  • Non-commutative harmonic oscillators and the connection problem for the heun differential equation Reviewed

    Hiroyuki Ochiai

    Letters in Mathematical Physics   70 ( 2 )   133 - 139   2004.12

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    We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than 1 and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.

    DOI: 10.1007/s11005-004-4292-5

  • Polynomials associated with the hypergeometric functions with finite monodromy groups Reviewed

    Hiroyuki Ochiai, Masaaki Yoshida

    International Journal of Mathematics   15 ( 7 )   629 - 649   2004.9

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    The hypergeometric equations with polyhedral monodromy groups derive 3-integral-parameter families of polynomials.

    DOI: 10.1142/S0129167X0400248X

  • Commuting Differential Operators of Type B2 Reviewed

    Hiroyuki Ochiai, Toshio Oshima

    Funkcialaj Ekvacioj   46 ( 2 )   297 - 336   2003.1

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    DOI: 10.1619/fesi.46.297

  • On coefficients of Yablonskii-Vorob'ev polynomials Reviewed

    Masanobu Kaneko, Hiroyuki Ochiai

    Journal of the Mathematical Society of Japan   55 ( 4 )   985 - 993   2003.1

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    We give a formula for the coefficients of the Yablonskii-Vorob'ev polynomial. Also the reduction modulo a prime number of the polynomial is studied.

    DOI: 10.2969/jmsj/1191418760

  • Intersection theory for loaded cycles IV - Resonant cases Reviewed

    Katsuhisa Mimachi, Hiroyuki Ochiai, Masaaki Yoshida

    Mathematische Nachrichten   260   67 - 77   2003

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    We study the structure of the twisted homology groups attached to weighted lines in the plane with resonant singular points, and find possible intersection pairings. As a typical example, we treat homology groups attached to 2-dimensional Selberg-type integrals.

    DOI: 10.1002/mana.200310105

  • Non-commutative harmonic oscillators and Fuchsian ordinary differential operators Reviewed

    Hiroyuki Ochiai

    Communications in Mathematical Physics   217 ( 2 )   357 - 373   2001.12

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    The spectral problem for non-commutative harmonic oscillators is shown to be equivalent to solve Fuchsian ordinary differential equations with four regular singular points in a complex domain.

    DOI: 10.1007/s002200100362

  • Bernstein degree and associated cycles of Harish-Chandra modules - Hermitian symmetric case Reviewed

    Kyo Nishiyama, Hiroyuki Ochiai, Kenji Taniguchi

    Asterisque   273   13 - 80   2001

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    Let G̃ be the metaplectic double cover of Sp(2n,ℝ), U(p,q) or O*(2p). we study the Bernstein degrees and the associated cycles of the irreducible unitary highest weight representations of G̃, by using the theta correspondence of dual pairs. The first part of this article is a summary of fundamental properties and known results of the Bernstein degrees and the associated cycles. Our first result is a comparison theorem between the K-module structures of the following two spaces; one is the theta lift of the trivial representation and the other is the ring of regular functions on its associated variety. Secondarily, we obtain the explicit values of the degrees of some small nilpotent KC-orbits by means of representation theory. The main result of this article is the determination of the associated cycles of singular unitary highest weight representations, which are the theta lifts of irreducible representations of certain compact groups. In the proofs of these results, the multiplicity free property of spherical subgroups and the stability of the branching coefficients play important roles.

  • The degrees of orbits of the multiplicity-free actions Reviewed

    Sholiei Kato, Hiroyuki Ochiai

    Asterisque   273   139 - 158   2001

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    We give a formula for the degrees of orbits of the irreducible representations with multiplicity-free action. In particular, we obtain the Bernstein degree and the associated cycle of the irreducible unitary highest weight modules of the scalar type for arbitrary hermitian Lie algebras.

  • Bernstein degree of singular unitary highest weight representations of the metaplectic group Reviewed

    K Nishiyama, H Ochiai

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   75 ( 2 )   9 - 11   1999.2

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  • A p-adic property of the Taylor series of exp(x + xp/p) Reviewed

    Hiroyuki Ochiai

    Hokkaido Mathematical Journal   28 ( 1 )   71 - 85   1999.1

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    The p-adic norms of the Taylor coefficients of the function exp(x + xp/p) are expressed in terms of a p-adic analytic function for p ≤ 23.

    DOI: 10.14492/hokmj/1351001078

  • Bernstein degree of singular unitary highest weight representations of the metaplectic group Reviewed

    Kyo Nishiyama, Hiroyuki Ochiai

    Proceedings of the Japan Academy Series A: Mathematical Sciences   75 ( 2 )   9 - 11   1999

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    DOI: 10.3792/pjaa.75.9

  • Quotients of some prehomogeneous vector spaces Reviewed

    Hiroyuki Ochiai

    Journal of Algebra   192 ( 1 )   61 - 73   1997.6

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    We give quotientsV//G=Spec(C[V]G) for some prehomogeneous vector spaces (G×H,V).

    DOI: 10.1006/jabr.1996.6979

  • Commuting differential operators of rank two Reviewed

    Hiroyuki Ochiai

    Indagationes Mathematicae   7 ( 2 )   243 - 255   1996.6

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    Commuting differential operators with symbols ∂21 + ∂22, ∂2122 are related to the functional equation V1(x1)U+(x1 + x2) + V1(x1)U-(x1 - x2) + V2(x2)U+(x1 + x2) - V2(x2)U-(x1 - x2) = F-(x1 + x2) + F-(x1 - x2) + G1(x1) + G2(x2). We discuss several properties, such as a meromorphic extension of solutions and periodicity, of this functional equation and commuting differential operators.

    DOI: 10.1016/0019-3577(96)85093-2

  • Characters and character cycles Reviewed

    Hiroyuki Ochiai

    Journal of the Mathematical Society of Japan   45 ( 4 )   583 - 598   1993

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    DOI: 10.2969/jmsj/04540583

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Books

  • シンメトリ

    ヘルマン・ワイル (著), 冨永 星(翻訳), 落合啓之(解説)(Role:Joint author)

    筑摩書房  2022.12 

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    Language:Japanese   Book type:General book, introductory book for general audience

    ワイルのこの最後の著書は数学のみならず物理、化学、建築にも広がる多彩な話題を取り扱っている。その啓蒙的な本に現れる数学的な内容を専門家として一般読者にわかりやすく解説した。

    DOI: 978-4480511386

  • Mathematical Basics of Motion and Deformation in Computer Graphics, Second Edition

    Ken Anjyo, Hiroyuki Ochiai(Role:Joint author)

    Morgan and Claypool  2017.4 

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    Language:English   Book type:Scholarly book

    DOI: https://doi.org/10.1007/978-3-031-02592-1

    Other Link: https://link.springer.com/book/10.1007/978-3-031-02592-1

  • Mathematical Progress in Expressive Image Synthesis II

    Hiroyuki Ochiai, Ken Anjyo(Role:Edit)

    Springer-Verlag  2015.6 

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    Language:English   Book type:Scholarly book

    Selected papers from the proceeding of MEIS2014

  • Mathematical Basics of Motion and Deformation in Computer Graphics

    Ken Anjyo, Hiroyuki Ochiai(Role:Joint author)

    Morgan & Claypool Publishers  2014.10 

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    Responsible for pages:doi:10.2200/S00599ED1V01Y201409CGR017   Language:English   Book type:Scholarly book

    The unique introduction of the mathematical background to the computer graphics

    Other Link: http://www.morganclaypool.com/doi/abs/10.2200/S00599ED1V01Y201409CGR017

  • Mathematical Progress in Expressive Image Synthesis I

    Ken Anjyo, Hiroyuki Ochiai(Role:Edit)

    Springer-Verlag  2014.8 

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    Language:English   Book type:Scholarly book

    Selected papers from the proceeding of MEIS2013

  • SL(2,R)の表現論

    落合 啓之

    朝倉書店  2024    ISBN:9784254118742

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    Language:Japanese  

    CiNii Books

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Presentations

  • A non-holonomic D-module with infinite-dimensional solutions Invited

    Hiroyuki Ochiai

    workshop "D-modules and hyperplane arrangements",  2023.2 

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    Event date: 2023.2

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Kyushu University   Country:Japan  

  • 2重旗多様体の軌道分解 Invited

    落合啓之

    研究集会「パーシステントホモロジーと表現論」  2023.2 

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    Event date: 2023.2

    Language:Japanese  

    Venue:オンライン   Country:Japan  

  • Math meets CG Invited International conference

    Hiroyuki Ochiai

    IPMU Colloquium  2023.2 

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    Event date: 2023.2

    Language:English   Presentation type:Oral presentation (general)  

    Venue:東京大学国際高等研究所カブリ数物連携宇宙研究機構   Country:Japan  

  • ゲームプログラマのための数学の歩き方 - ベクトル解析編

    長谷川勇, 鍛冶静雄, 落合啓之

    CEDEC2022  2022.8 

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    Event date: 2022.8

    Language:Japanese  

    Venue:パシフィコ横浜ノース   Country:Japan  

    リアルやアニメの3Dのコンピュータゲームの制作を行っているプログラマやエンジニアに向けた数学の専門家からのわかりやすい解説と応用を与えた。IMIとして、鍛冶教授、溝口教授とも共同で、何年にもわたって続けている。

  • ガウス全集に記載されている算術幾何平均と超幾何関数 Invited

    落合啓之

    研究集会 Low dimensional topology and number theory XIII  2022.3 

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    Event date: 2022.3

    Language:Japanese  

    Venue:九州大学   Country:Japan  

  • Opening the black box of mathematics for CG International conference

    Hiroyuki Ochiai, Ken Anjyo

    SIGGRAPH ASIA 2021  2021.12 

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    Event date: 2021.12

    Language:English   Presentation type:Oral presentation (general)  

    Venue:東京国際フォーラム   Country:Japan  

  • ゲームプログラマのための数学の歩き方 - デュアルクォータニオン編

    長谷川勇, 鍛冶静雄, 落合啓之

    CEDEC2021  2021.8 

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    Event date: 2021.8

    Language:Japanese  

    Venue:パシフィコ横浜   Country:Japan  

  • An absolute version of Hasse zeta functions Invited International conference

    Hiroyuki Ochiai

    Riemann-Roch in characteristic one and related topics  2019.10 

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    Event date: 2019.10 - 2020.10

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Johns Hopkins University   Country:United States  

  • 超幾何関数のリー環対称性について Invited

    落合啓之

    研究集会「微分方程式と表現論」  2018.12 

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    Event date: 2018.12 - 2019.12

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:城西大学   Country:Japan  

  • Making a bridge between Ibukiyama and Kobayashi Invited International conference

    Hiroyuki Ochiai

    第20回整数論オータムワークショップ  2017.9 

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    Event date: 2017.9

    Language:English   Presentation type:Oral presentation (general)  

    Venue:ホテルアベスト八方アルディラ   Country:Japan  

  • Zeros of Eulerian polynomials Invited International conference

    Hiroyuki Ochiai

    Various Aspects of Multiple Zeta Functions  2017.8 

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    Event date: 2017.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:名古屋大学   Country:Japan  

  • Covariant differential operators and Heckman-Opdam hypergeometric systems Invited International conference

    Hiroyuki Ochiai

    International Conference for Korean Mathematical Society 70th Anniversary,  2016.10 

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    Event date: 2016.10

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Seoul National University   Country:Korea, Republic of  

    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。

  • An Elementary Introduction to Matrix Exponential for CG International conference

    Hiroyuki Ochiai, Ken Anjyo and Ayumi Kimura

    SIGGRAPH  2016.7 

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    Event date: 2016.7

    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Venue:Anaheim Convention Center   Country:United States  

  • An Introduction to Matrix Exponential for CG Invited International conference

    Hiroyuki Ochiai, Ken Anjyo

    2016.2 

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    Event date: 2016.2

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Weta Digital, NZ   Country:New Zealand  

  • 概説講演“CG 映像制作におけるリー理論” Invited

    落合啓之

    表現論シンポジウム  2015.11 

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    Event date: 2015.11

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:静岡県伊豆の国市   Country:Japan  

  • CG映像制作の数理 Invited

    落合 啓之

    日本数学会  2015.9 

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    Event date: 2015.9

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:京都産業大学   Country:Japan  

  • 共変微分作用素の超幾何多項式表示 Invited

    落合 啓之

    不変性と双対性  2015.9 

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    Event date: 2015.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:鹿児島大学理学部   Country:Japan  

  • Computer graphics and mathematics Invited International conference

    落合 啓之

    Computational and Geometric Approaches for Nonlinear Phenomena  2015.8 

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    Event date: 2015.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:早稲田大学   Country:Japan  

  • Covariant differential operators and Heckman–Opdam hypergeometric systems Invited International conference

    落合 啓之

    Analytic Representation Theory of Lie Groups  2015.7 

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    Event date: 2015.7

    Language:English   Presentation type:Oral presentation (general)  

    Venue:東京大学Kavli IPMU   Country:Japan  

  • Mathematical basics of motion and deformation in computer graphics International conference

    Ken Anjyo, Hiroyuki Ochiai

    ACM SIGGRAPH  2014.8 

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    Event date: 2014.8

    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Venue:Vancouver   Country:Canada  

    This is a course lecture on mathematical basics to graphics community

  • 行列の数理と運動の記述 Invited

    落合 啓之

    Computer Entertainment Developer Conference 2013  2013.8 

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    Event date: 2013.8

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:パシフィコ横浜,   Country:Japan  

    ゲーム開発者を中心とした実業界で活躍するエキスパートに向けて、数学的手法や思想、特に行列やリー群を活用した、運動の記述や補間について、分かりやすく解説した。

  • ユニタリ表現の分類はそろそろできるだろうか? Invited

    落合 啓之

    2013 年度日本数学会年会  2013.3 

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    Event date: 2013.3

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:京都大学   Country:Japan  

  • Double flag variety for a symmetric pair and finiteness of orbits Invited International conference

    OCHIAI HIROYUKI

    Representation Theory of Chevalley Groups and Related Topics  2012.3 

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    Event date: 2012.3

    Language:English   Presentation type:Oral presentation (general)  

    Venue:名古屋大学大学院多元数理科学研究科   Country:Japan  

  • Positivity of alpha determinant Invited International conference

    OCHIAI HIROYUKI

    Geometrci Analysis on Euclidean Homogeneous Spaces  2012.1 

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    Event date: 2012.1

    Language:English  

    Country:Japan  

  • On Sekiguchi correspondence Invited International conference

    Hiroyuki Ochiai

    Topics in the Theory of Weyl Groups and Root Systems  2011.9 

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    Event date: 2011.9

    Presentation type:Oral presentation (general)  

    Venue:東京大学大学院数理科学研究科   Country:Japan  

    Kostant-Sekiguchi correspondence, so called, is the bijective correspondence between the set of nilpotent (co)adjoint orbits on a semisimple Lie algebra and the set of nilpotent KC-orbits on the complexified tangent space of the corresponding Riemannian symmetric space.
    From the beginning of the theory, Sekiguchi has the correspondence on the context of non-Riemannian semisimple symmetric spaces. I will review this Sekiguchi's work, as well as an application/ interpretation to the geometric invariants of representation theory.

    Other Link: http://www.gem.aoyama.ac.jp/~rtweb/workshop/sekiguchi60/program_sekiguchi60.html

  • On non-commutative harmonic oscillators Invited International conference

    Hiroyuki Ochiai

    Infinite Analysis 11  2011.7 

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    Event date: 2011.7

    Presentation type:Oral presentation (general)  

    Venue:東京大学大学院数理科学研究科   Country:Japan  

    Other Link: http://sites.google.com/site/infiniteanalysis2011/program

  • Positivity of an alpha determinant Invited International conference

    OCHIAI HIROYUKI

    Analysis, Geometry and Group Representations for Homogeneous Spaces  2010.11 

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    Event date: 2010.11

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Lorentz Center, Leiden University   Country:Netherlands  

  • Invariant hyperfunctions on some semisimple symmetric space Invited International conference

    OCHIAI HIROYUKI

    International conference on representation theory and harmonic analysis  2010.6 

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    Event date: 2010.6

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Chern Institute of Mathematics in Nankai, 天津   Country:China  

  • Invariant hyperfunctions on some semisimple symmetric spaces, Invited International conference

    落合啓之

    Workshop on Harmonic Analysis and Invariant Distributions,  2009.12 

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    Event date: 2009.12

    Presentation type:Oral presentation (general)  

    Venue:National University of Singapore,   Country:Singapore  

    12/14 と 12/16 の2コマの連続講演

  • Zeta functions and Casimir energies on infinite symmetric groups, Invited International conference

    落合啓之、黒川信重

    Casimir Force, Casimir Operators and the Riemann Hypothesis,  2009.11 

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    Event date: 2009.11

    Presentation type:Oral presentation (general)  

    Venue:九州大学西新プラザ   Country:Japan  

  • An algebraic transformation of Gauss hypergeometric function Invited International conference

    落合啓之

    Differential equations and symmetric spaces  2009.1 

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    Event date: 2009.1

    Presentation type:Oral presentation (general)  

    Venue:駒場キャンパス数理棟会議場   Country:Japan  

    An algebraic transformation of Gauss hypergeometric function

  • Fractional differential equations and symmetry Invited International conference

    Hiroyuki Ochiai

    Colloquium  2023.7 

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    Event date: 2024.5

    Language:English   Presentation type:Oral presentation (general)  

    Venue:National University of Mongolia   Country:Mongolia  

  • Divergent series and summation formula Invited International conference

    Hiroyuki Ochiai

    Freshmen math seminar  2023.5 

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    Event date: 2023.6 - 2024.5

    Language:English   Presentation type:Oral presentation (general)  

    Venue:モンゴル国立大学   Country:Mongolia  

  • Nilpotent orbits in complex simple Lie algebras and prehomogeneous vector spaces Invited International conference

    Hiroyuki Ochiai

    研究集会 ``Representation theory of reductive Lie groups and algebras''  2019.3 

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    Event date: 2019.3

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  • Gamma factors of Selberg's zeta functions and absolute zeta functions Invited

    落合啓之

    研究集会「多重三角関数とその一般化」  2018.3 

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    Event date: 2018.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:神戸大学   Country:Japan  

  • An Introduction to Matrix Exponential for CG Invited International conference

    Ken Anjyo, Hiroyuki Ochiai

    2016.2 

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    Event date: 2016.2

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Victoria University of Wellington, NZ   Country:Japan  

  • 特殊関数の活用について Invited

    落合 啓之

    第6回多重ゼータミニセミナー  2013.2 

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    Event date: 2013.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  • Alpha-determinant for rank-two matrices International conference

    OCHIAI HIROYUKI

    International Conference on Geometry, Number Theory and Representation Theory  2012.10 

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    Event date: 2012.10

    Language:English  

    Venue:Inha University, Korea   Country:Korea, Republic of  

  • Double flag variety for a symmetric pair and spherical actions Invited International conference

    OCHIAI HIROYUKI

    Summer School and Workshop on Representation Theory and Harmonic Analysis  2012.6 

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    Event date: 2012.6

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Chern Institute of Mathematics, Nankai University, China   Country:China  

  • Non-commutative harmonic oscillators and the connection problem for the Heun differential equation Invited International conference

    Hiroyuki Ochiai

    Workshop on "Avoided ? Crossing of Eigenvalue Curves" -- Non-commutative Harmonic Oscillator, Special Functions and Number Theory--  2012.3 

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    Event date: 2012.3

    Presentation type:Oral presentation (general)  

    Venue:九州大学、稲盛ホール   Country:Japan  

    In this talk, I will talk about the relation between the spectral
    problem of the non-commutative harmonic oscillator of size two in the
    positive elliptic case and the second order ordinary differential
    equation on the complex projective line with an accessory parameter, so
    called Heun's equation. I also mention the multiplicity of the discrete
    spectrum of the non-commutative harmonic oscillator in the `odd sector'.

  • 対称対の有限型二重旗多様体 Invited

    落合啓之

    Symposium on Representation Theory 2011  2011.11 

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    Event date: 2011.11

    Presentation type:Oral presentation (invited, special)  

    Venue:国民宿舎 紀州路みなべ   Country:Japan  

    簡約代数群 G の部分旗多様体と, その対称部分群 K の部分旗多様体の直積を
    対称対の2重旗多様体と呼ぶことにする.
    2重旗多様体への K の対角的な作用が有限個の軌道を持つのはどんな部分旗多様体の組のときか,
    また, その場合に軌道分解はどうなるか, という問題を考える.
    この講演は, 西山享, 近藤健介の講演へと引き続く, 概説的な部分を担当する.
    この講演の内容は, 上記2名ならびに, 谷口健二, Xuhua He との共同研究の内容に基づく.

  • Mathematical consideration on visualization of complex objects Invited International conference

    Hiroyuki Ochiai

    International Symposium on Plasma Turbulence, Imaging and Synergy  2011.6 

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    Event date: 2011.6

    Presentation type:Oral presentation (general)  

    Venue:伊藤極限プラズマ研究連携センター   Country:Japan  

  • Zeros of Witten zeta functions and absolute limits Invited International conference

    Nobushige Kurokawa and Hiroyuki Ochiai

    Noncommutative Geometry and Arithmetic  2011.3 

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    Event date: 2011.3

    Presentation type:Oral presentation (general)  

    Venue:Johns Hopkins University, 日米数学研究所   Country:United States  

  • 状態和としての多重ゼータ値 Invited

    Hiroyuki Ochiai

    RIMS 研究集会「多重ゼータ値の諸相」  2011.5 

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    Event date: 2010.9

    Presentation type:Oral presentation (general)  

    Venue:京都大学数理解析研究所   Country:Japan  

  • アルファ行列式の正値性について Invited

    落合 啓之

    RIMS 研究集会「等質空間と非可換調和解析」  2010.6 

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    Event date: 2010.6

    Language:English   Presentation type:Oral presentation (general)  

    Venue:京都大学数理解析研究所   Country:Japan  

  • Polynomial differential operators acting on automorphic forms, I, II, Invited International conference

    落合啓之

    Workshop on Invariant Theory and Related Topics,  2010.2 

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    Event date: 2010.2

    Presentation type:Oral presentation (general)  

    Venue:Inha University, Korea   Country:Korea, Republic of  

    2/17と2/19 の2コマの連続講演

  • Invariant distributions, a survey,

    落合啓之

    2009年度表現論ワークショップ,  2009.12 

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    Event date: 2009.12

    Presentation type:Oral presentation (general)  

    Venue:鳥取市、とりぎん文化会館,   Country:Japan  

  • Polynomial solutions of a generalization of Gelfand hypergeometric equations,

    落合啓之

    Zatas and Limit Laws in Okinawa 2009,  2009.11 

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    Event date: 2009.11

    Presentation type:Oral presentation (general)  

    Venue:フェストーネ、宜野湾市,   Country:Japan  

  • マーラー測度の一つの高次元化 Invited

    落合啓之

    解析数論セミナー  2009.9 

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    Event date: 2009.9

    Presentation type:Oral presentation (general)  

    Venue:名古屋大学   Country:Japan  

    Higher Mahler measures

  • 変数分離 Invited

    落合啓之

    名古屋大学数学教育セミナー  2009.7 

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    Event date: 2009.7

    Presentation type:Oral presentation (general)  

    Venue:名古屋大学   Country:Japan  

    Separation of variables

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MISC

  • 総和法 Reviewed

    落合啓之

    数学セミナー, 日本評論社   2023.8

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    Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (scientific journal)  

    特集「1+2+3+... = -1/12」

  • ワイル「シンメトリ」解説 Reviewed

    落合啓之

    筑摩書房   2022.12

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    Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (scientific journal)  

  • 表現論 Reviewed

    落合啓之

    数理科学   2020.10

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    Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (scientific journal)  

    特集「現代数学の捉え方 代数編」

  • Discriminants, Resultants, and Multidimensional Determinants

    落合啓之

    日本評論社   2020.4

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    Language:Japanese   Publishing type:Book review, literature introduction, etc.  

    数学セミナー増刊「数学好きの人のためのブックガイド」第3章「名著・大著を読む」

  • Arithmetic structure of CMSZ fake projective planes Reviewed

    Fumiharu Kato, Hiroyuki Ochiai

    JOURNAL OF ALGEBRA   2006.11

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    We show that the fake projective planes that are constructed from dyadic discrete subgroups discovered by Cartwright, Mantero, Steger, and Zappa are realized as connected components of certain unitary Shimura surfaces. As a corollary we show that these fake projective planes have models defined over the number field Q(root-3,root 5). (c) 2006 Published by Elsevier Inc.

    DOI: 10.1016/j.jalgebra.2006.07.019

  • Arithmetic structure of CMSZ fake projective planes

    Fumiharu Kato, Hiroyuki Ochiai

    JOURNAL OF ALGEBRA   2006.11

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    Language:English  

    We show that the fake projective planes that are constructed from dyadic discrete subgroups discovered by Cartwright, Mantero, Steger, and Zappa are realized as connected components of certain unitary Shimura surfaces. As a corollary we show that these fake projective planes have models defined over the number field Q(root-3,root 5). (c) 2006 Published by Elsevier Inc.

    DOI: 10.1016/j.jalgebra.2006.07.019

  • Scaling Limit of Successive Approximations for w(1) = -w(2) Reviewed

    Tetsuya Hattori, Hiroyuki Ochiai

    FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA   2006.8

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    We prove existence of scaling limits of sequences of functions defined by the recursion relation w(n+1)(1) (x) = -w(n)(x)(2). which is a successive approximation to w(1) (x) = -w(x)(2), a simplest non-linear ordinary differential equation whose solutions have moving singularities. Namely, the sequence approaches the exact solution as n -> infinity in an asymptotically conformal way, w(n)(x) asymptotic to q(n)w(-)(q(n)-x), for a sequence of numbers {q(n)} and a function w(-). We also discuss implication of the results in terms of random sequential bisections of a rod.

    DOI: 10.1619/fesi.49.291

  • Invariant distributions on a non-isotropic pseudo-Riemannian symmetric space of rank one

    Hiroyuki Ochiai

    Indagationes Mathematicae   2005.12

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    We investigate the structure of invariant distributions on a non-isotropic non-Riemannian symmetric space of rank one. Especially, the J-criterion related to the generalized Gelfand pair is shown for this space without imposing the condition on the eigenfuction of the Laplace-Bertrami operator. © 2005 Royal Netherlands Academy of Arts and Sciences.

    DOI: 10.1016/S0019-3577(05)80043-6

  • Invariant distributions on a non-isotropic pseudo-Riemannian symmetric space of rank one

    H Ochiai

    INDAGATIONES MATHEMATICAE-NEW SERIES   2005.12

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    We investigate the structure of invariant distributions on a non-isotropic non-Riemannian symmetric space of rank one. Especially, the J-criterion related to the generalized Gelfand pair is shown for this space without imposing the condition on the eigenfuction of the Laplace-Bertrami operator.

    DOI: 10.1016/S0019-3577(05)80043-6

  • Non-commutative harmonic oscillators and the connection problem for the heun differential equation

    Hiroyuki Ochiai

    Letters in Mathematical Physics   2004.12

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    We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than 1 and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.

    DOI: 10.1007/s11005-004-4292-5

  • Non-commutative harmonic oscillators and the connection problem for the heun differential equation

    H Ochiai

    LETTERS IN MATHEMATICAL PHYSICS   2004.11

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    Language:English  

    We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than I and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.

    DOI: 10.1007/s11005-004-4292-5

  • Polynomials associated with the hypergeometric functions with finite monodromy groups

    H Ochiai, M Yoshida

    INTERNATIONAL JOURNAL OF MATHEMATICS   2004.9

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    The hypergeometric equations with polyhedral monodromy groups derive 3-integral-parameter families of polynomials.

    DOI: 10.1142/S0129167X0400248X

  • Polynomials associated with the hypergeometric functions with finite monodromy groups

    H Ochiai, M Yoshida

    INTERNATIONAL JOURNAL OF MATHEMATICS   2004.9

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    The hypergeometric equations with polyhedral monodromy groups derive 3-integral-parameter families of polynomials.

    DOI: 10.1142/S0129167X0400248X

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Works

  • 表現論における積分と特殊関数

    2007

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  • 多変数マーラー測度の研究

    2007

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Professional Memberships

  • 日本アクチュアリ会

  • Japan Mathematical Society

  • MSJ

  • 日本数学会

  • 日本数学会

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Committee Memberships

  • 内閣府 ムーンショット 目標1「2050年までに、人が身体、脳、空間、時間の制約から解放された社会を実現」   アドバイザ  

    2020 - Present   

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    Committee type:Government

    researchmap

  • 日本数学会   Journal of Mathematical Society of Japan 編集委員  

    2019 - Present   

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    Committee type:Academic society

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  • JST さきがけ「数学と情報科学で解き明かす多様な対象の数理構造と活用」   アドバイザ  

    2019 - Present   

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    Committee type:Government

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Academic Activities

  • さきがけ/領域アドバイザ

    Role(s): Review, evaluation

    JST  2019.6 - 2024.6

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    Type:Scientific advice/Review 

  • co-chair International contribution

    MEIS2015  ( Japan ) 2015.9

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    Type:Competition, symposium, etc. 

  • 科研費1段審査委員(審査委員表彰を受けた, 2017年秋)

    Role(s): Review, evaluation

    日本学術振興会  2015.6 - 2017.6

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    Type:Scientific advice/Review 

  • co-chair International contribution

    MEIS2014  ( Japan ) 2014.11

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    Type:Competition, symposium, etc. 

    Number of participants:78

  • co-organizer International contribution

    Prehomogeneous Vector Spaces and Related Topics  ( Japan ) 2014.9

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    Type:Competition, symposium, etc. 

  • 評議員

    日本数学会  ( Japan ) 2010.3 - 2011.2

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    Type:Competition, symposium, etc. 

  • 函数解析分科会分科会委員

    日本数学会  ( Japan ) 2007.4 - 2010.3

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    Type:Competition, symposium, etc. 

  • 第2段審査委員、審査第三部会、数物系科学・化学小委員会

    Role(s): Review, evaluation

    学振  2007.1 - 2007.12

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    Type:Scientific advice/Review 

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Research Projects

  • A new data-driven approach to bring humanity into virtual worlds with computer vision

    Grant number:23K28129  2023.4 - 2026.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    THOMAS DIEGO, 鍛冶 静雄, 古賀 靖子, 川崎 洋, 落合 啓之

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    Grant type:Scientific research funding

    The core idea is to leverage RGB-D data to achieve realism of digital humans. We propose:
    (1) Weakly supervised method to learn 3D shape from in-the-wild RGB-D data.
    (2) Real-time animation model to learn motion from RGB-D videos.
    (3) Data-driven method to learn semantically appropriate body movements.

    CiNii Research

  • 「かたち」と「うごき」を表す高次元データ記述子の開発

    Grant number:22H05107  2022.6 - 2027.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Transformative Research Areas (A)

    平岡 裕章, 石井 豊, 池 祐一, 落合 啓之

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    Grant type:Scientific research funding

    現代社会に氾濫する高次元データは,その構造を直接「見る」ことができない.低次元空間への射影や断面を用いる従来法からは,構造の直感的理解を得ることは難しく,さらには幾何・トポロジー構造が潰されたものになる問題点もある.そこで本研究では,高次元データを直感的に知覚できるデータ記述子の開発を目標に据えた,以下の3テーマを実施する.
    テーマ1:バーチャルリアリティ(VR)を用いたインタラクティブな高次元可視化の数理
    テーマ2:パーシステントホモロジーの代数解析・代数幾何的研究とその応用
    テーマ3:マグニチュードホモロジーの自然言語処理・オミックスデータ解析への応用

    CiNii Research

  • データ記述科学の創出と諸分野への横断的展開

    Grant number:22A201  2022 - 2026

    Japan Society for the Promotion of Science・Ministry of Education, Culture, Sports, Science and Technology  Grants-in-Aid for Scientific Research  Grant-in-Aid for Transformative Research Areas (A)

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    Authorship:Coinvestigator(s)  Grant type:Scientific research funding

  • 特殊関数論の圏化

    Grant number:17K18726  2017 - 2018

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 特殊関数論の圏化

    Grant number:17K18726  2017 - 2018

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Challenging Research(Exploratory)

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • 表現論と特殊関数論の統合的展開

    Grant number:15H03613  2015 - 2019

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 表現論と特殊関数論の統合的展開

    Grant number:15H03613  2015 - 2019

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • 映像の特徴抽出空間の構成

    Grant number:26610026  2014 - 2016

    Grants-in-Aid for Scientific Research  Grant-in-Aid for challenging Exploratory Research

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • 映像の特徴抽出空間の構成

    Grant number:26610026  2014 - 2016

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 動く映像の特徴抽出空間の構成

    Grant number:23654054  2011 - 2013

    Grants-in-Aid for Scientific Research  Grant-in-Aid for challenging Exploratory Research

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • 動く映像の特徴抽出空間の構成

    Grant number:23654054  2011 - 2013

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • デジタル映像数学の構築と表現技術の革新

    2010.10 - 2016.3

    JST(科学技術振興機構) 

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    Authorship:Coinvestigator(s) 

    コンピュータグラフィックスに代表されるデジタル映像の応用は拡大の一途をたどっています.
    本研究は,作りやすさや効率を重視しつつ,従来よりさらに豊かな表現力を持つ映像の制作を可能にするために,デジタル映像表現を対象とする新たな数学分野形成の礎を築くことを目指します.
    特に,人間の動作や表情と流体の表現に焦点をあて,これらの映像表現の数学的特徴づけと,作り手の意図をより的確に反映できる数学モデルの構築を推進します.

  • デジタル映像数学の構築と表現技術の革新

    2010 - 2015

    Grants-in-Aid for Scientific Research  クレスト(科学技術振興機構)

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    Authorship:Coinvestigator(s)  Grant type:Competitive funding other than Grants-in-Aid for Scientific Research

  • 表現論における積分と特殊関数

    Grant number:19204011  2007 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A)

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    Authorship:Principal investigator  Grant type:Scientific research funding

  • 表現論における積分と特殊関数

    Grant number:19204011  2007 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 多変数マーラー測度の研究

    Grant number:19654003  2007 - 2009

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 実簡約群の表現の幾何学的不変量と積分変換

    Grant number:15340005  2003 - 2006

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 非可換調和振動子と特殊関数

    Grant number:15654020  2003 - 2005

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 等質空間のプランシェレル公式

    Grant number:15634007  2003

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 簡約群の幾何学的表現論

    Grant number:11440011  1999 - 2001

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 拡張された帯球函数の微分方程式系

    Grant number:09740122  1997 - 1998

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • オイラーポアソン方程式の対称性

    Grant number:08740121  1996

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 無限次元リ一環の指標と微分方程式

    Grant number:05230055  1993

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 実半単純代数群の指標の幾何的側面

    Grant number:04740097  1992

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Grant type:Scientific research funding

  • 半単純対称空間の表現論に現われる特殊関数の研究

    Grant number:02740090  1990

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

      More details

    Grant type:Scientific research funding

▼display all

Educational Activities

  • I give courses for undergraduate and those for graduate students.

Class subject

  • 数理科学特論4

    2024.10 - 2025.3   Second semester

  • 数理科学特別講義Ⅳ

    2024.10 - 2025.3   Second semester

  • 数学共創基礎Ⅴ

    2024.10 - 2024.12   Fall quarter

  • 数学特論7

    2024.4 - 2024.9   First semester

  • 組合せ論大意

    2024.4 - 2024.9   First semester

  • 数学特論12

    2023.10 - 2024.3   Second semester

  • 複素解析学大意

    2023.10 - 2024.3   Second semester

  • 数学特論B2

    2023.10 - 2023.12   Fall quarter

  • 数学共創基礎Ⅴ

    2023.10 - 2023.12   Fall quarter

  • 数学演習AⅡ

    2022.10 - 2023.3   Second semester

  • 線形代数学Ⅱ

    2022.10 - 2023.3   Second semester

  • 数学共創基礎Ⅴ

    2022.10 - 2022.12   Fall quarter

  • 数学特論12(複素解析学)

    2022.4 - 2022.9   First semester

  • 複素解析学大意

    2022.4 - 2022.9   First semester

  • 線形代数学Ⅰ

    2022.4 - 2022.9   First semester

  • 数学演習AⅠ

    2022.4 - 2022.9   First semester

  • 数学演習AⅡ

    2021.10 - 2022.3   Second semester

  • 線形代数学Ⅱ

    2021.10 - 2022.3   Second semester

  • 数学共創基礎Ⅴ

    2021.10 - 2021.12   Fall quarter

  • 数学特論1(代数幾何学)

    2021.4 - 2021.9   First semester

  • 数理科学特別講義Ⅹ

    2021.4 - 2021.9   First semester

  • 代数幾何学大意

    2021.4 - 2021.9   First semester

  • 線形代数学Ⅰ

    2021.4 - 2021.9   First semester

  • 数学演習AI

    2021.4 - 2021.9   First semester

  • 数理科学特論10

    2021.4 - 2021.9   First semester

  • 代数幾何学大意

    2020.10 - 2021.3   Second semester

  • 数学特論1

    2020.10 - 2021.3   Second semester

  • 数学演習ⅠB

    2020.10 - 2021.3   Second semester

  • 線形代数学・同演習B

    2020.10 - 2021.3   Second semester

  • 線形代数学・同演習A

    2020.4 - 2020.9   First semester

  • 数学演習ⅠA

    2020.4 - 2020.9   First semester

  • 線形代数学・同演習B

    2019.10 - 2020.3   Second semester

  • 複素解析学大意

    2019.4 - 2019.9   First semester

  • 線形代数続論

    2019.4 - 2019.9   First semester

  • 数学特論12

    2019.4 - 2019.9   First semester

  • 線形代数学・同演習A

    2019.4 - 2019.9   First semester

  • 複素関数論

    2018.10 - 2019.3   Second semester

  • 数学ⅠB

    2018.10 - 2019.3   Second semester

  • 数学ⅠC

    2018.10 - 2019.3   Second semester

  • 数学特論12

    2018.4 - 2018.9   First semester

  • 線形代数続論

    2018.4 - 2018.9   First semester

  • 複素解析学大意

    2018.4 - 2018.9   First semester

  • 線形代数続論

    2018.4 - 2018.9   First semester

  • 数学概論Ⅲ・演習

    2017.10 - 2018.3   Second semester

  • 数理科学特別講義Ⅳ

    2017.10 - 2018.3   Second semester

  • 数学概論III

    2017.10 - 2018.3   Second semester

  • 複素関数論

    2017.4 - 2017.9   First semester

  • 数学ⅠB

    2017.4 - 2017.9   First semester

  • 数学ⅠC

    2017.4 - 2017.9   First semester

  • 表現論基礎・演習

    2017.4 - 2017.9   First semester

  • 数学IB

    2017.4 - 2017.9   First semester

  • 表現論基礎演習

    2017.4 - 2017.9   First semester

  • 数学概論III

    2016.10 - 2017.3   Second semester

  • 表現論大意

    2016.4 - 2016.9   First semester

  • 微分積分学III

    2015.10 - 2016.3   Second semester

  • 微分積分学II

    2015.10 - 2016.3   Second semester

  • 表現論大意

    2015.4 - 2015.9   First semester

  • 微分積分学I

    2015.4 - 2015.9   First semester

  • MMAモデル理論

    2014.10 - 2015.3   Second semester

  • 微分積分学III

    2014.10 - 2015.3   Second semester

  • 微分積分学II

    2014.10 - 2015.3   Second semester

  • 微分積分学I

    2014.4 - 2014.9   First semester

  • 表現論大意

    2014.4 - 2014.9   First semester

  • 表現論基礎演習

    2013.10 - 2014.3   Second semester

  • MMAモデル理論

    2013.10 - 2014.3   Second semester

  • 代数学1

    2013.4 - 2013.9   First semester

  • 数学III

    2013.4 - 2013.9   First semester

  • MMAモデル理論

    2012.10 - 2013.3   Second semester

  • 表現論大意

    2012.10 - 2013.3   Second semester

  • 数学III

    2012.4 - 2012.9   First semester

  • 数学Ib

    2012.4 - 2012.9   First semester

  • 代数学1

    2012.4 - 2012.9   First semester

  • 表現論大意

    2011.10 - 2012.3   Second semester

  • 微分積分学

    2011.10 - 2012.3   Second semester

  • 微分積分学

    2011.4 - 2012.3   Full year

  • 微分積分学

    2011.4 - 2011.9   First semester

  • 数学Ib

    2011.4 - 2011.9   First semester

  • 線形代数続論

    2011.4 - 2011.9   First semester

  • 線形代数

    2010.4 - 2011.3   Full year

  • 微分方程式大意

    2010.4 - 2010.9   First semester

  • 線形代数続論

    2010.4 - 2010.9   First semester

  • 数学IB 複素関数論

    2010.4 - 2010.9   First semester

  • 線形代数

    2010.4 - 2010.9   First semester

  • 情報III

    2009.10 - 2010.3   Second semester

  • 数理科学特別講義Ⅳ

    2024.10 - 2025.3   Second semester

  • 数理科学特論4

    2024.10 - 2025.3   Second semester

  • 数学共創基礎Ⅴ

    2024.10 - 2024.12   Fall quarter

  • 数理学基礎論究

    2024.4 - 2025.3   Full year

  • 数理学基礎講究Ⅰ

    2024.4 - 2025.3   Full year

  • 数理学基礎講究Ⅱ

    2024.4 - 2025.3   Full year

  • 数学特論7

    2024.4 - 2024.9   First semester

  • 組合せ論大意

    2024.4 - 2024.9   First semester

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FD Participation

  • 2022.4   Role:Participation   Title:数理学府FD

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2021.7   Role:Participation   Title:数理学府FD

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2021.3   Role:Participation   Title:数理学府FD

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2019.7   Role:Participation   Title:数理学府FD

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2014.12   Role:Participation   Title:ルーブリック

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2014.7   Role:Participation   Title:GPA

    Organizer:[Undergraduate school/graduate school/graduate faculty]

  • 2010.4   Role:Participation   Title:新任教員研修

    Organizer:University-wide

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Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.

  • 2023  大阪公立大学  Classification:Intensive course  Domestic/International Classification:Japan 

    Semester, Day Time or Duration:2023.10.16-20

  • 2014  東京大学大学院数理科学研究科  Classification:Intensive course  Domestic/International Classification:Japan 

    Semester, Day Time or Duration:前期

  • 2014  東北大学大学院理学研究科  Classification:Intensive course  Domestic/International Classification:Japan 

    Semester, Day Time or Duration:前期

Other educational activity and Special note

  • 2022  Class Teacher  学部

  • 2020  Class Teacher  学部

  • 2019  Class Teacher  学部

  • 2014  Class Teacher  全学

Outline of Social Contribution and International Cooperation activities

  • I got Award as a Reviewer for JSPS grant.

Social Activities

  • CEDEC AWARDS 2022 優秀賞

    CEDEC2021  横浜市  2021.8

     More details

    Audience:General, Scientific, Company, Civic organization, Governmental agency

    Type:Seminar, workshop

    「ゲームプログラマのための数学の歩き方」シリーズとして、スクエアエニックスの長谷川氏、IMIの鍛冶教授と共同で、ゲーム産業に用いられている数学の肝をわかりやすく伝える講演を行った。

  • 糸島サイエンスキャラバン「日常に隠れている数学」

    福岡県糸島市  糸島市役所  2018.12

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    Audience:General, Scientific, Company, Civic organization, Governmental agency

    Type:Lecture

    小学生やお年寄りもたくさん含む糸島市民向けの講演会。

  • 「コンピュータグラフィックスと数学」

    日本数学会  岡山大学  2018.9

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    Audience:General, Scientific, Company, Civic organization, Governmental agency

    Type:Lecture

    日本数学会の市民講演会。高校生などを含む一般市民への広報活動。

  • 招待講演「行列の数理と運動の記述」

    Computer Entertainment Developer Conference 2013  パシフィコ横浜,  2013.8

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    Audience:General, Scientific, Company, Civic organization, Governmental agency

    Type:Lecture

    ゲーム開発者を中心とした実業界で活躍するエキスパートに向けて、数学的手法や思想、特に行列やリー群を活用した、運動の記述や補間について、分かりやすく解説した。

  • 数学科大学入試問題研究会, 高大連携,

    愛知県高等学校数学研究会, 名城大学  2010.6

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    Audience:Infants, Schoolchildren, Junior students, High school students

    Type:Seminar, workshop

  • 講演:「渋滞学の数理」数学の玉手箱2, 2008.4.26. 「ブルバキ、20 世紀のユークリッド原論」新・数学の玉手箱, 2008.10.25;

    NHK 文化センター  NHK文化センター名古屋  2010.5

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    Audience:General, Scientific, Company, Civic organization, Governmental agency

    Type:Lecture

  • 「大学入試講評」高大連携

    三重県高等学校数学教育研究会, 津西高校,  2008.5

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    Audience:Infants, Schoolchildren, Junior students, High school students

    Type:Seminar, workshop

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Media Coverage

  • 特集「使える!数学」 Newspaper, magazine

    週刊ダイヤモンド16年1月23日号  2016.1

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    特集「使える!数学」

  • 氏名入りで研究の紹介。 https://www.sankei.com/west/news/160113/wst1601130003-n3.html Newspaper, magazine

    産経新聞2015年12月31日  2015.12

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    氏名入りで研究の紹介。
    https://www.sankei.com/west/news/160113/wst1601130003-n3.html

  • 記事「輝数遇数 : 数学教室訪問(7)落合啓之 代数解析学・とくに表現論に現れる特殊関数」において紹介された。 Newspaper, magazine

    現代数学2015年11月号  2015.11

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    記事「輝数遇数 : 数学教室訪問(7)落合啓之 代数解析学・とくに表現論に現れる特殊関数」において紹介された。

  • 記事「ε-δがわからない」を執筆。従来よく行われている切り口とは、別の面を提示した意欲的なもの Newspaper, magazine

    数学セミナー6月号 2015  2015.6

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    記事「ε-δがわからない」を執筆。従来よく行われている切り口とは、別の面を提示した意欲的なもの

  • 不変式と表現論、特集「表現論の世界」 Newspaper, magazine

    数理科学2013 年1 月号, pp26–33.  2013.1

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    不変式と表現論、特集「表現論の世界」

  • 名著・大著を読む「判別式、終結式、行列式」Gelfand, Kapranov, Zelevinsky Newspaper, magazine

    数学セミナー  2011.8

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    名著・大著を読む「判別式、終結式、行列式」Gelfand, Kapranov, Zelevinsky

  • 4月号「てらかんと歩む」 Newspaper, magazine

    「数学セミナー」日本評論社  2010.3

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    4月号「てらかんと歩む」

  • 「現代数学の巨大パズルを解く/デービット・ヴォーガン(David Vogan) 氏インタビュー」 Newspaper, magazine

    数学セミナー  2008.2

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    「現代数学の巨大パズルを解く/デービット・ヴォーガン(David Vogan) 氏インタビュー」

  • Aperitif「講演を聴く」 Newspaper, magazine

    数学セミナー  2007.12

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    Aperitif「講演を聴く」

  • Aperitif「ただいま建設中」 Newspaper, magazine

    数学セミナー  2007.6

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    Aperitif「ただいま建設中」

  • 「表現論と特殊関数」 Newspaper, magazine

    数学セミナー  2007.3

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    「表現論と特殊関数」

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Activities contributing to policy formation, academic promotion, etc.

  • 2023.4 - 2027.3   科学技術振興機構

    科学技術振興機構創発的研究支援事業永江パネル創発アドバイザー

  • 2022.4 - 2025.3   日本学術振興会

    日本学術振興会学術システム研究センター数物系科学専門調査班専門研究員

  • 2020.6 - 2025.6   内閣府、日本学術振興会

    ムーンショット研究開発プログラムの目標1「2050年までに、人が身体、脳、空間、時間の制約から解放された社会を実現」のアドバイザ

Acceptance of Foreign Researchers, etc.

  • テクニオン

    Acceptance period: 2016.3 - 2015.3   (Period):2weeks to less than 1 month

    Nationality:Israel

    Business entity:Ministry of education

  • OLMデジタル

    Acceptance period: 2015.5 - 2015.6   (Period):1 month or more

    Nationality:France

    Business entity:On-campus funds

Travel Abroad

  • 2016.7

    Staying countory name 1:United States   Staying institution name 1:Anaheim Convention Center

  • 2015.2 - 2015.3

    Staying countory name 1:New Zealand   Staying institution name 1:Victoria University

  • 2014.2

    Staying countory name 1:New Zealand   Staying institution name 1:Victoria University