Toshinori Oaku (大阿久 俊則)
Japanese page
Research interests: Algebraic analysis
- Algebraic study of systems of linear partial differential equations
and generalized functions
- Algorithms and programming for D-modules
My favorite free software for symbolic computation
Programs
- bsi :
a Risa/Asir program for computing local and global
Bernstein-Sato ideals of polynomial mappings.
- annlog :
a Risa/Asir program for computing the annihilator of
f^s(\log f)^m for a polynomial f.
Preprints and unpublished papers
- T. Oaku:
On various b-functions of specializable D-modules.
to appear in RIMS Kokyuroku.
PDF
- T. Oaku:
Bernstein-Sato polynomials and analytic non-equivalence of plane curve singularities.
PDF
- T. Oaku:
Length and multiplicity of the local cohomology with support
in a hyperplane arrangement.
arXiv
published as a part of
'Localization, local cohomology, and the b-function of a D-module
with respect to a polynomial'
Advanced Studies in Pure Mathematics 77 (2018), pp. 353-398.
Publications
- T. Oaku:
An algorithmic study on the integration of holonomic hyperfunctions
--oscillatory integrals and a phase space integral
associated with a Feynman diagram.
RIMS Kokyuroku Bessatsu B75 (2019), pp. 41-60.
PDF
- T. Oaku:
An attempt to compute holonomic systems for Feynman integrals in
two-dimensional space-time.
RIMS Kokyuroku, Kyoto Univ., Vol. 2101, pp. 77-90, 2019.
PDF
- T. Oaku:
Localization, local cohomology, and the b-function of a D-module
with respect to a polynomial.
Advanced Studies in Pure Mathematics 77 (2018), pp. 353-398.
PDF
- T. Oaku:
Algorithms for D-modules, integration, and generalized functions with applications to
statistics.
Advanced Studies in Pure Mathematics 77 (2018), pp. 253-352.
PDF
- T. Oaku:
Operational calculus for holonomic distributions in the framework of D-module theory.
RIMS Kokyuroku Bessatsu B61 (2017), pp. 123--140.
arXiv
PDF file
- T. Oaku:
Annihilators of Laurent coefficients of the complex power for
normal crossing singularity.
RIMS Kokyuroku Bessatsu B57 (2016), pp. 79--84.
arXiv
PDF file
- N. Marumo, T. Oaku, A. Takemura:
Properties of powers of functions satisfying second-order linear differential equations with applications to statistics.
Japan Journal of Industrial and Applied Mathematics: Volume 32, Issue 2 (2015), 553-572.
Preprint:
arXiv
- T. Oaku:
Annihilators of distributions associated with algebraic local cohomology of a hypersurface.
Complex Variables and Elliptic Equations 59 (2014), 1533-1546.
PDF
-
T. Oaku:
Algorithms for integrals of holonomic functions over domains defined by
polynomial inequalities.
Journal of Symbolic Computation 50 (2013), 1--27.
http://dx.doi.org/10.1016/j.jsc.2012.05.004.
arXiv:1108.4853v2[cs.SC]
PDF file
Errata
- T. Oaku:
An algorithm to compute the differential equations
for the logarithm of a polynomial.
In Proceedings of
the 37th International Conference on
Symbolic and Algebraic Computation
(ISSAC 2012),
pages 273--280. ACM Press, 2012.
arXiv:1201.3198v1[cs.SC]
PDF file
- R. Bahloul, T. Oaku: Local Bernstein-Sato ideals: algorithm and examples.
J. Symbolic Computation 45 (2010), 46-59.
arXiv:0806.4869
PDF file
- T. Oaku: Regular b-functions of D-modules.
J. Pure and Applied Algebra 213 (2009), 1545-1557.
PDF file
- M. Granger, T. Oaku, N. Takayama: Tangent cone algorithm for homogenized differential operators.
J. Symbolic Computation 39 (2005), 417-431.
PDF file
- M. Granger, T. Oaku:
Minimal filtered free resolutions for analytic D-modules.
J. Pure and Applied Algebra 191 (2004), 157-180.
PDF file
- T. Oaku, Y.Shiraki, N.Takayama:
Algebraic algorithms for D-modules and numerical analysis.
Computer mathematics (Proceedings of ASCM 2003), 23--39,
Lecture Notes Ser. Comput., 10, World Sci. Publ., River Edge, NJ, 2003.
PDF file .
- T. Oaku:
Minimal free resolutions of analytic D-modules.
Proceedings of the 10th International Conference on Complex Analysis,
Pusan, Korea, 2002, pp. 145-151.
PDF file
- T. Oaku, N. Takayama: Minimal free resolutions of homogenized D-modules.
J. Symbolic Computation 32 (2001), 575-595.
PDF file
- T. Oaku, N. Takayama, H. Tsai: Polynomial and rational solutions of
holonomic systems.
J. Pure and Applied Algebra 164 (2001), 199-220.
arXiv:math/0001064
- T. Oaku, N. Takayama: Algorithms for D-modules --restriction,
tensor product, localization, and local cohomology groups.
J. Pure and Applied Algebra 156 (2001), 267-308.
PDF file
- T. Oaku, N. Takayama, U. Walther: A localization algorithm
for D-modules.
J. Symbolic Computation 29 (2000), 721-728.
arXiv:math/9811030
- T. Oaku, N. Takayama: An algorithm for de Rham cohomology
groups of the complement of an affine variety.
J. Pure and Applied Algebra 139 (1999), 201-233.
. arXiv:math/9801114
- T. Oaku, S. Yamazaki: Higher-codimensional boundary value
problems and F-mild microfunctions --Local and microlocal
uniqueness--.
Publication of the Research Institute for
Mathematical Sciences, Kyoto Univ. 34 (1998), 383-437 .
- T. Oaku: Algorithms for b-functions, restrictions, and
algebraic local cohomology groups of D-modules.
Advances in Applied Math. 19 (1997), 61-105.
PDF file
Errata
- T. Oaku: Algorithms for the b-function and D-modules
associated with a polynomial.
J. Pure Appl. Algebra 117 & 118 (1997), 495-518.
PDF file
- T. Oaku: An algorithm of computing b-functions.
Duke Math. J. 87 (1997), 115-132.
PDF file
- T. Oaku: Groebner bases for D-modules on a non-singluar affine
algebraic variety.
Tohoku Math. J. 48 (1996), 575-600.
- T. Oaku: Algorithmic methods for Fuchsian systems of linear partial
differential equations.
J. Math. Soc. Japan 47 (1995), 297-328 .
-
T. Oaku, T. Shimoyama:
A Groebner basis method for modules over rings of differential
operators.
J. Symbolic Computation 18 (1994), 223-248.
-
T. Oaku:
Computation of the characteristic variety and the singular locus
of a system of differential equations with polynomial coefficients.
Japan J. Indust. Appl. Math. 11 (1994), 485-497.
PDF
-
T. Oaku:
Boundary value problem for Fuchsian partial differential equations
and reflection of singularities.
Banach Center Publications 27 (1992), 337-348.
PDF
-
T. Oaku:
Some remarks on local solvability of Fuchsian partial differential
equations for hyperfunctions.
Yokohama Math. J. 37 (1989), 139-143.
PDF
-
T. Oaku:
Local solvability of Fuchsian elliptic equations for hyperfunctions.
Yokohama Math. J. 36 (1988), 109-114.
PDF
-
T. Oaku:
Higher codimensional boundary value problem and F-mild hyperfunctions.
In: Algebraic Analysis, eds M. Kashiwara, T. Kawai, Academic Press,
1988, pp. 571-586.
-
T. Oaku:
Removable singularities of solutions of linear partial differential equations : Systems and Fuchsian equations.
J. Fac. Sci. Univ. Tokyo 33 (1986), 403-428.
doi/10.15083/00039504
-
T. Oaku:
Boundary value problems for systems of linear partial differential
equations and propagation of micro-analyticity.
J. Fac. Sci. Univ. Tokyo 33 (1986), 175-232.
doi/10.15083/00039506
-
T. Oaku:
Microlocal boundary value problem for Fuchsian operators, I.
-F-mild microfunctions and uniqueness theorem.
J. Fac. Sci. Univ. Tokyo 32 (1985), 287-317.
doi/10.15083/00039518
-
T. Oaku:
F-mild hyperfunctions and Fuchsian partial differential equations.
Advanced Studies in Pure Mathematics 4 (1984), 223-242.
PDF
-
T. Oaku:
Analytic hypo-ellipticity and propagation of regularity for a system
of microdifferential equations with non-involutory characteristics.
Math. Ann. 269 (1984), 145-168.
DigiZeitschriften
-
T. Oaku:
A canonical form of a system of microdifferential equations with
non-involutory characteristics and branching of singularities.
Inventiones Math. 65 (1982), 491-525.
DigiZeitschriften
-
T. Oaku:
Micro-local Cauchy problems and local boundary value problems.
Proc. Japan Acad. 55 (1979), 136-140.
PDF
Slides of talks
-
T. Oaku:
A naive approach to microlocal analysis of Feynman amplitudes.
Recent topics in algebraic analysis, February 21, 2022,
Chiba University.
-
T. Oaku:
Computation of holonomic systems for Feynman amplitudes
associated with some simple diagrams.
The Mathematics of Linear Relations between Feynman Integrals
Mainz Institute for Theoretical Physics, March 18-22, 2019.
-
T. Oaku:
On various b-functions of specializable D-modules.
Various Problems of Algebraic Analysis.
RIMS, Kyoto University, October 15-19, 2018.
-
T. Oaku:
An attempt to compute holonomic systems for Feynman integrals in two-dimensional
space-time.
Microlocal analysis and asymptotic analysis.
RIMS, Kyoto University, October 16-20, 2017.
-
T. Oaku:
An algorithmic study on the intgration of holonomic distributions.
New development of microlocal analysis and singular perturbation theory,
RIMS, Kyoto University, October 3-7, 2016.
-
T. Oaku:
Some algorithmic problems for holonomic distributions.
Microlocal Analysis and Singular Perturbation Theory,
RIMS, Kyoto University, October 5-9, 2015.
-
T. Oaku:
Algorithms for D-modules, integration, and generalized functions.
The 8th Mathematical Society of Japan Seasonal Institute
"Current Trends on Groebner Bases
-The 50th Anniversary of Groebner Bases-",
Hotel Nikko Osaka, Osaka, Japan,
July 1-10, 2015.
chapter 1 ,
chapter 2 ,
chapter 3 ,
chapter 4 ,
chapter 5
-
T. Oaku:
Some D-module theoretic aspects of the local cohomology of a polynomial ring.
The 8th Mathematical Society of Japan Seasonal Institute
"Current Trends on Groebner Bases
-The 50th Anniversary of Groebner Bases-",
Hotel Nikko Osaka, Osaka, Japan,
July 1-10, 2015.
-
T. Oaku:
Algebraic and algorithmic study of some generalized functions
associated with a real polynomial (or a real analytic function)
Seminar at the department of algebra, the University of Sevilla, Spain,
September, 2014.
-
T. Oaku:
Algorithms for D-modules applied to generalized functions.
Summer school
"Algebra, Algorithms and Algebraic Analysis", Rolduc Abbey,
the Netherlands, September 2-6, 2013.
-
T. Oaku:
An algorithm to compute the differential equations
for the logarithm of a polynomial.
the 37th International Conference on
Symbolic and Algebraic Computation
(ISSAC 2012),
Grenoble, July 2012.
e-mail: oaku at lab.twcu.ac.jp