# Hiroaki Terao

Last updated: Apr 7, 2017 at 10:57

Name Hiroaki Terao http://www.math.sci.hokudai.ac.jp/~terao/ Hokkaido University Faculty of Science Vice President, Deputy Executive Director, Professor 90119058

## Research Areas

Apr 2015
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Today
Professor Emeritus, Faculty of Science, Hokkaido University

Oct 2016
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Mar 2017
Deputy Executive Director, Institute for International Collaboration, Hokkaido University

Oct 2016
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Mar 2017
Director, Center for International Education and Research, Institute for International Collaboration, Hokkaido University

Oct 2016
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Mar 2017
Director, Overseas Office Coordination Unit, Institute for International Collaboration, Hokkaido University

Oct 2016
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Mar 2017
Professor, Institute for International Collaboration, Hokkaido University

Apr 2015
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Mar 2017
Vice President, Hokkaido University

Mar 2016
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Sep 2016
Director, Center for the Advancement of Global Education, Office of International Affairs, Hokkaido University

Oct 2015
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Sep 2016
Deputy Executive Director, Office of International Affairs, Hokkaido University

Apr 2015
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Sep 2016
Professor, Office of International Affairs, Hokkaido University

Apr 2015
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Feb 2016
Director, International Student Center, Office of International Affairs, Hokkaido University

Apr 2013
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Mar 2015
Dean, Faculty of Science / School of Science, Hokkaido University

Apr 2011
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Mar 2015
Dean, Graduate School of Science, Hokkaido University

Apr 2006
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Mar 2015
Professor, Faculty of Science, Hokkaido University

Apr 2005
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Mar 2006
Professor, Tokyo Metropolitan University

Apr 1998
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Mar 2005
Professor, Tokyo Metropolitan University

Jul 1996
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Mar 1998
Professor, Hokkaido University

Aug 1993
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May 1999
Professor, Deparment of Mathematics, University of Wisconsin-Madison

Jun 1990
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May 1993
Associate Professor, Deparment of Mathematics, University of Wisconsin-Madison

Apr 1985
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Sep 1991
Associate Professor, International Christian University

Apr 1981
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Mar 1985
Assistant Professor, International Christian University

Apr 1979
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Mar 1981
Instructor, International Christian University

Apr 1977
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Mar 1979
Assistant, International Christian University

## Education

Mar 1981

Kyoto University, D. Sc.

Apr 1976
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Mar 1977
the University of Tokyo

Apr 1974
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Mar 1976
the University of Tokyo, M. Sc.

Apr 1970
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Mar 1974
School of Science, the University of Tokyo

## Committee Memberships

Oct 2014
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Today
Sicence Council of Japan  Member

Sep 2013
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Today
Research Institute for Mathematical Sciences (RIMS), Kyoto University  Technical Committee

Sep 2013
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Aug 2015
Research Institute for Mathematical Sciences (RIMS), Kyoto University  Advisory Board

Oct 2009
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Jun 2015
MSJ Science Committee  Science Committee

Jul 2011
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Jun 2013
MSJ Science Committee  Science Committee, Chair

Apr 2011
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Mar 2013
JSPS Research Center for Science Systems  Senior Program Officer

Apr 2010
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Mar 2011
JSPS Research Center for Science Systems  Program Officer

## Published Papers

GAO Ruimei, PEI Donghe, TERAO Hiroaki
Proceedings of the Japan Academy. Ser. A, Mathematical Sciences   88 41-45   2012   [Refereed]
T. Abe, H. Terao, A. Wakamiko
Advances in Math.   230 2364-2377   2012   [Refereed]
Daisuke Suyama, Hiroaki Terao
Bull. London Math. Soc.   44 563-570   2012   [Refereed]
The braid arrangement is the Coxeter arrangement of the type . The Shi arrangement is an affine arrangement of hyperplanes consisting of the hyperplanes of the braid arrangement and their parallel translations. In this paper, we give an...
Arrangements stable under the Coxeter groups
H. Kamiya, A. Takemura, H. Terao
in: Configuration Spaces: Geometry, Topology and Combinatorics,'' Proceedings of a special period at the De Giorgi Center, Scuola Normale in Pisa, May - June, 2010, (ed. A. Bjorner, F. Cohen, C. De Concini, C. Procesi, M. Salvetti)   327-354   2012   [Refereed]
Kamiya Hidehiko, Takemura Akimichi, Terao Hiroaki
Advances in Applied Mathematics   47(2) 379-400   Aug 2011   [Refereed]
We consider the problem of counting the number of possible sets of rankings (called ranking patterns) generated by unfolding models of codimension one. We express the ranking patterns as slices of the braid arrangement and show that all braid slic...
Abe Takuro, Terao Hiroaki
Journal of Algebra   330 251-262   Mar 2011   [Refereed]
We define primitive derivations for Coxeter arrangements which may not be irreducible. Using those derivations, we introduce the primitive filtrations of the module of invariant logarithmic differential forms for an arbitrary Coxeter arrangement w...
Abe Takuro, Terao Hiroaki
European J. Combin.   32(8) 1191-1198   2011   [Refereed]
Kamiya Hidehiko, Takemura Akimichi, Terao Hiroaki
Annals of Combinatorics   15 449-464   2011   [Refereed]
The characteristic quasi-polynomials of the arrangements of root systems and mid-hyperplane arrangements
Kamiya Hidehiko, Takemura Akimichi, Terao Hiroaki
Progress in Math.   283 177-190   2010   [Refereed]
Takuro Abe, Hiroaki Terao
Math. Z.   264 813-828   2010   [Refereed]
Let be a finite irreducible real reflection group, which is a Coxeter group. We explicitly construct a basis for the module of differential 1-forms with logarithmic poles along the Coxeter arrangement by using a primitive derivation. As a c...
T. Abe, H. Terao, M. Yoshinaga
Proc. Amer. Math. Soc.   137(4) 1405-1410   2009   [Refereed]
T. Abe, H. Terao, M. Wakefield
J. London Math. Soc.   77(2) 335-348   2008   [Refereed]
Hiroaki Terao
Proc. Amer. Math. Soc.   136 2639-2639   2008   [Refereed]
Kamiya Hidehiko, Takemura Akimichi, Terao Hiroaki
J. Alg. Combin.   27 317-330   2008   [Refereed]
Hiroaki Terao
Advances in Math.   214 366-378   2007   [Refereed]
Let be a nonempty real central arrangement of hyperplanes and be the set of chambers of . Each hyperplane defines a half-space and the other half-space . Let . For $H... T. Abe, H. Terao, M. Wakefield Advances in Math. 215 825-838 2007 [Refereed] H. Kamiya, P. Orlik, A. Takemura, H. Terao Annals of Combinatorics 10 219-235 2006 [Refereed] Hiroaki Terao Manuscripta Math. 118 1-9 2005 [Refereed] The Hodge filtration of the module of derivations on the orbit space of a finite real reflection group acting on an -dimensional Euclidean space was introduced and studied by K. Saito. The filtration is equivalent data to the flat structu... Hiroaki Terao Proc. AMS 133 2029-2034 2005 [Refereed] In [5] (=Terao, H.: Multiderivations of Coxeter arrangements. Inventiones math., 148 (2002) 659--674), we constructed a basis for the contact-order filtration of the module of derivations on the orbit space of a finite real reflection group act... Hiroki Horiuchi, Hiroaki Terao Journal of Algebra 266 169-179 2003 [Refereed] Let be a finite set of nonzero linear forms in several variables with coefficients in a field of characteristic zero. Consider the -algebra of rational functions on V which are regular outside$\bigcu...
Hiroaki Terao
Topology and its appl.   118 255-274   2002   [Refereed]
Hiroaki Terao
Inventiones math.   148 659-674   2002   [Refereed]
Let be an -dimensional Euclidean space. Let be a finite irreducible orthogonal reflection group. Let be the corresponding Coxeter arrangement. Let be the algebra of polynomial functions on For $H \... Hiroaki Terao Journal of Algebra 250 549-558 2002 [Refereed] Let be a finite set of nonzero linear forms in several variables with coefficients in a field of characteristic zero. Consider the -algebra of rational functions generated by$\{1/\alpha \mid \alpha \...
Logarithmic forms and anti-invariant forms of reflection groups
Hiroaki Terao, Anne V. Shepler
Advanced Studies in Pure Math.   27 273-278   2000   [Refereed]
The double Coxeter arrangements
L. Solomon, H. Terao
Comment. Math. Helv.   73 237-258   1998   [Refereed]
The determinant of a hypergeometric period matrix
A. Douai, H. Terao
Inventiones Math.   128 417-436   1997   [Refereed]
K. Aomoto, M. Kita, P. Orlik, H. Terao
Advances in Math.   128 119-152   1997   [Refereed]
Lee Ki-Suk, Terao Hiroaki
Journal of mathematical sciences, the University of Tokyo   3 83-89   1996   [Refereed]
A (central) arrangement is a finite family of one codimensional subspaces of a vector space . Relations between the module of logarithmic forms of and the module of logarithmic forms of are studied. It is found ...
Hiroaki Terao, Sergey Yuzvinsky
Nagoya mathematical journal   139 129-149   Sep 1995   [Refereed]
Arrangements and Milnor fibers
Orlik Peter, Terao Hiroaki
Math. Ann.   301 211-235   1995   [Refereed]
The number of critical points of a product of powers of linear functions
Peter Orlik, Hiroaki Terao
Inventiones Math.   120 1-14   1995   [Refereed]
Local systems on complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors
V. Schechtman, H. Terao, A. Varchenko
J. Pure and Applied Alg.   100 93-102   1995   [Refereed]
Michael Falk, Hiroaki Terao
Transactions AMS   349 189-202   1997   [Refereed]
We study cohomology with coefficients in a rank one local system on the
complement of an arrangement of hyperplanes . The cohomology plays an
important role for the theory of generalized hypergeometric functions. We
combine several known resul...
Peter Orlik, Hiroaki Terao
Nagoya mathematical journal   134 65-73   Jun 1994   [Refereed]
Free arrangements and relation spaces
Keith Brandt, Hiroaki Terao
Discrete Comput. Geom.   12 49-63   1994   [Refereed]
Peter Orlik, Hiroaki Terao
Tohoku mathematical journal. Second series   45(3) 369-383   Sep 1993   [Refereed]
A Coxeter arrangement is the set of reflecting hyperplanes in the reflection representation of a finite Coxeter group. Arnold and Saito showed that every Coxeter arrangement is free. We prove that any restriction of a Coxeter arrangement is again ...
Terao Hiroaki
Tohoku mathematical journal. Second series   41(2) 237-247   Jun 1989
Terao Hiroaki
Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics   30(2) 379-391   Dec 1983
TERAO Hiroaki
Publications of the Research Institute for Mathematical Sciences   17 657-663   Sep 1981
Terao Hiroaki
Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics   27(2) 313-320   Aug 1980
Terao Hiroaki
Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics   27(2) 293-312   Aug 1980
Terao Hiroaki
Scientific papers of the College of General Education, University of Tokyo   28 153-158   1978

## Misc

KAMIYA HIDEHIKO, TAKEMURA AKIMICHI, TERAO HIROAKI

RIMS Kokyuroku   742 70-78   Jan 1991

RIMS Kokyuroku   474 88-97   Dec 1982
TERAO Hiroaki
RIMS Kokyuroku   735 129-139   Dec 1990
TERAO HIROAKI
RIMS Kokyuroku   281 106-119   Oct 1976
TERAO Hiroaki
RIMS Kokyuroku   634 25-39   Dec 1987

## Books etc

 Senkei daisu kogi to enshu.Masanori Kobayashi; Hiroaki Terao; (Part:Joint Work)Baifukan.   Feb 2014   ISBN:4563004871
 Invariants and symmetry (Fuhenryou to taishousei) (Chikuma Gakugei Bunko)Jun Imai, Hiroaki Terao, Hiroaki Nakamura (Part:Joint Work)Chikuma Shobou   Mar 2013   ISBN:4480095217
 Arrangements of Hyperplanes - Sapporo 2009 (Advanced Studies in Pure Mathematics 62)Hiroaki Terao, Sergey Yuzvinsky (Part:Joint Editor)Mathematical Society of Japan   Dec 2011   ISBN:4931469671
 The state and a prospect of applied singularity theory : March 16-17, 2009Research Center for Intergrative Mathematics, Hokkaido University, Shyuichi Izumiya, Goo Ishikawa, Hiroaki TeraoResearch Center for Intergrative Mathematics, Hokkaido University   2009
 Linear Algebra - Lectures and Exercises (Senkei Daisuu - Kougi to Enshuu) (Japanese)Masanori Kobayashi, Hiroaki Terao (Part:Joint Work)Baifuukan   Apr 2007   ISBN:4563003735
 What are the invariants? (Fuhenryou to wa nani ka?) (Bluebacks) (Japanese)Jun Imai, Hiroaki Nakamura, Hiroaki Terao (Part:Joint Work)Kodansha   Nov 2002   ISBN:4062573938
 Arrangements and hypergeometric integrals (JMS Memoir 9)Peter Orlik, Hiroaki Terao (Part:Joint Work)Mathematical Society of Japan   2001   ISBN:9784931469105
 Arrangements -- Tokyo 1998 (Advanced Studies in Pure Mathematics 27)Michael Falk, Hiroaki Terao (Part:Joint Editor)紀伊国屋書店   2000   ISBN:4314101407
 Arrangements of Hyperplanes (Grundlehren der mathematischen Wissenschaften)Peter Orlik, Hiroaki Terao (Part:Joint Work)Springer-Verlag   1992   ISBN:3540552596

## Conference Activities & Talks

Subarrangements and restrictions of Weyl arrangements [Invited]
Hiroaki Terao
the Special Session on "Topology and Combinatorics of Arrangements (in honor of Mike Falk)" at an AMS Spring Eastern Sectional Meeting   19 Mar 2016
Multiple addition theorem on arrangements of hyperplanes and a proof of the Shapiro-Steinberg-Kostant-Macdonald dual-partition formula [Invited]
Hiroaki Terao
Braids, Configuration Spaces, and Quantum Topology   8 Sep 2015
Before and After the Ideal-free Theorem [Invited]
Hiroaki Terao
Hyperplane arrangements and re ection groups   11 Aug 2015
On Parabolic Subarrangements and Restrictions of Weyl arrangements [Invited]
Hiroaki Terao
Differential and combinatorial aspects of singularities   7 Aug 2015
Ideal Free Theorem and Saturated Free Filtrations os Affine Weyl Arrangements [Invited]
Hiroaki Terao
Computational Geometric Topology in Arrangement Theory   10 Jul 2015
Ideal Free Theorem and Saturated Free Filtrations of AffineWeyl Arrangements [Invited]
Hiroaki Terao
Algebraic structures in combinatorics and geometry   11 Jun 2015
Arrangements of hyperplanes and applications [Invited]
Hiroaki Terao
13 Mar 2015
Ideal Free Theorem and Saturated Free Filtrations of Affine Weyl Arrangements [Invited]
Hiroaki Terao
The 10th Kagoshima Algebra-Analysis-Geometry Seminar   17 Feb 2015
Free ltrations of affine arrangements of infinitely many hyperplanes [Invited]
Hiroaki Terao
Hokkaido University - University of Bremen Joint Seminar "Arrangements of Hyperplanes"   1 Dec 2014
Multiple addition theorem on arrangements of hyperplanes and a proof of the Shapiro-Steinberg-Kostant-Macdonald dual-partition formula [Invited]
Hiroaki Terao
The 1st Workshop of JSPS-MAE Sakura Program "Geometry and Combinatorics of Hyperplane Arrangements and Related Problems"   3 Sep 2014
Ideals of the roots posets and a new proof of the dual-partition formula by Shapiro-Steinberg-Kostant-Macdonlald [Invited]
Hiroaki Terao
"The 2nd Franco-Japanese-Vietnamese Symposium on Singularities"   26 Aug 2014
Chambers of Arrangements and Arrow's Impossibility Theorem
Hiroaki Terao
Workshop at "Recent developments on geometrical and algebraic methods in Economics"   22 Aug 2014
On ideal subarrangements of Weyl arrangements [Invited]
Hiroaki Terao
The 13th International Workshop in Real and Complex Singularities   28 Jul 2014
On ideal subarrangements of Weyl arrangements [Invited]
Hiroaki Terao
FPSAC '14 (The 26th International Conference on Formal Power Series and Algebraic Combinatorics)   30 Jun 2014
The freeness of ideal-Shi arrangements and free paths in affine Weyl arrangements (and a question) [Invited]
Hiroaki Terao
Workshop on \New perspectives in hyperplane and re ection arrangements"   10 Feb 2014
On ideal subarrangements of Weyl arrangements [Invited]
Hiroaki Terao
CIMPA-UNESCO-MESR-MINECO-VIETNAM research school on "Geometry and Topology of Singular Varieties. Theory and Applications"   2 Dec 2013
On ideal subarrangements of Weyl arrangements [Invited]
Hiroaki Terao
Conference on "Japanese Turkish Joint Geometry Meeting"   22 Nov 2013
On ideal subarrangements of Weyl arrangements. [Invited]
Hiroaki Terao
Conference on "Hyperplane arrangements and characteristic classes"   12 Nov 2013
The freeness of ideal subarrangements of Weyl arrangements
Hiroaki Terao
Combinatorics Seminar   25 Jul 2013
Multiple addition/deletion theorems and the existence of free paths in the affine Weyl arrangements
Hiroaki Terao
Combinatorics Seminar   11 Jul 2013
The freeness of ideal subarrangements of Weyl arrangements [Invited]
Hiroaki TERAO
Conference on "The 6th Pacific RIM Conference on Mathematics 2013”   2 Jul 2013
Logarithmic derivation modules of Shi arrangements associated with root systems [Invited]
Hiroaki Terao
Conference on "Hyperplane Arrangements: Combinatorial and Geometric Aspects"   21 Feb 2013
Logarithmic derivation modules of Shi arrangements associated to root systems [Invited]
Hiroaki Terao
Workshop on "Free Divisors and Differential Equations"   8 Nov 2012
Logarithmic derivation modules of Shi arrangements associated to root systems [Invited]
Hiroaki Terao
Combinatorial Representation Theory and Related Topics   11 Oct 2012
Primitive derivations, Shi arrangements and Bernoulli polynomials [Invited]
Hiroaki Terao
Colloquium   28 Sep 2012
Primitive derivations, Shi arrangements and Bernoulli polynomials [Invited]
Hiroaki Terao
2012 Shanghai Conference on Algebraic Combinatorics   20 Aug 2012
Primitive derivations, Shi arrangements, Bernoulli polynomials and the height-free conjecture [Invited]
Hiroaki Terao
FPSAC '12 (The 24th International Conference on Formal Power Series and Algebraic Combinatorics)   2 Aug 2012
Height basis of Weyl arrangements [Invited]
Hiroaki Terao
the "Arrangements in Pyrenees" School on hyperplane arrangements and related topics   11 Jun 2012
Primitive derivations, Shi arrangements and Bernoulli polynomials [Invited]
Hiroaki Terao
the Special Session on "Singularities, Stratifications and their Applications" at an AMS Sectional Meeting   3 Mar 2012
Simple bases for the logarithmic derivation modules of the generalized Shi arrangements [Invited]
Hiroaki Terao
Topics in the Theory of Weyl Groups and Root Systems (Sekiguchi 60)   20 Sep 2011
The Shi arrangements and the Bernoulli numbers [Invited]
Hiroaki Terao
the Special Session on "The Algebraic Geometry and Topology of Hyperplane Arrangements" at an AMS Sectional Meeting   9 Apr 2011
Combinatorial and algebro-geometric properties of free arrangements [Invited]
Hiroaki Terao
Workshop on "Algebra and Geometry of Configuration Spaces and related structures   22 Jun 2010
Mathematics related to hyperplane arrangements [Invited]
Hiroaki Terao
special one-hour lecture by an Algebra Prize recipient, MSJ Annual Meeting   26 Mar 2010
Mathematics related to hyperplane arrangements
Hiroaki Terao
Geometry of singularities and related topics   13 Mar 2010
Periodicity of hyperplane arrangements with integral coefficients modulo positive integers
Hiroaki Terao
Finite Groups, vertex operator algebras and combinatorics   6 Jan 2009
Totally free arrangements of hyperplanes
Hiroaki Terao
Conference in Honour of Peter Orlik   19 Aug 2008
On the free multiarrangements
Hiroaki Terao
Millican Lecture, Colloquium   2 May 2008
On the free multiarrangements
Hiroaki Terao
Several Aspects of Hyperplane Arrangements, 1037TH American Mathematical Society Meeting, special session on Arrangements and Related Topics   28 Mar 2008
Periodicity of integral arrangements modulo positive integers
Hiroaki Terao
Several Aspects of Hyperplane Arrangements   4 Feb 2008
The characteristic quasi-polynomial of integral arrangements and root systems
Hiroaki Terao
CIMPA summer school ALS \& S 2007, Arrangements and Local Systems,   15 Jun 2007
The characteristic polynomials of (multi)arrangements
Hiroaki Terao
CIMPA summer school ALS \& S 2007, Arrangements and Local Systems   15 Jun 2007
Chambers of arrangements of hyperplanes and Arrow's impossibility theorem
Hiroaki Terao
Braids and their Ramifications - Configuration Spaces, Arrangements, Mapping, Mapping-Class groups, 3-Manifolds   24 May 2007
Chambers of arrangements of hyperplanes and Arrow's impossibility theorem
Hiroaki Terao
American Mathematical Society, Annual Meeting, special session on Arrangements and Related Topics   6 Jan 2007
Basic properties of multiarrangements
Hiroaki Terao
Geometry and analysis on complex varieties   13 Dec 2006
Chambers of arrangements of hyperplanes and Arrow's impossibility theorem
Hiroaki Terao
Colloquium   9 Nov 2006
Chambers of arrangements of hyperplanes and Arrow's impossibility theorem
Hiroaki Terao
Development of Computational Algebraic Statistics   8 Nov 2006
Multiderivations of Coxeter Arrangements of Type and Primitive Derivations
Hiroaki Terao
Geometry and Analysis on Complex Algenbraic Varieties, Joint RFBR-JSPS Symposium   17 Aug 2006
On the Catalan numbers
Hiroaki Terao
a talk at Hokkaido University for high school students.   31 Jul 2006
Various phases of arrangements of hyperplanes
Hiroaki Terao
Colloquium   28 Apr 2006
Multiderivations of real reflection arrangements
Hiroaki Terao
The international symposium on singularity theory and their applications II   10 May 2006
Multiderivations of Coxeter Arrangements of Type and Primitive Derivations
Hiroaki Terao
Colloquium   17 Feb 2006
Introduction to hyperplane arrangements - Especially on free arrangements -
Hiroaki Terao
Recent Topics on Real and Complex Singularities   28 Nov 2005
What makes arrangements free?
Hiroaki Terao
Euroconferences in Mathematics on Crete, Algebraic and Geometric Combinatorics   21 Aug 2005
Arrangements of hyperplanes and hypergeometric integrals
Hiroaki Terao
Applications of singularities workshop   7 Feb 2005
Free arrangements of hyperplanes
Hiroaki Terao
Periods -Around the Theory of Primitive Forms- In Honor of Professor Kyoji Saito on his Sixtieth Birthday   26 Jan 2005

## Research Grants & Projects

Ministry of Education, Culture, Sports, Science and Technology: Grant-in-Aid for Exploratory Research
Project Year: 2014 - 2016    Investigator(s): Hiroaki TERAO
Ministry of Education, Culture, Sports, Science and Technology: Grant-in-Aid for Challenging Exploratory Research
Project Year: 2011 - 2013    Investigator(s): Hiroaki TERAO
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(B)
Project Year: 2010 - 2012    Investigator(s): Shyuichi IZUMIYA
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(B)
Project Year: 2009 - 2011    Investigator(s): Hiroaki TERAO
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 2008 - 2010    Investigator(s): Toshitake KOHNO
We determined the structure of the image of the monodromy representations of mapping class groups in conformal field theory. We proved that the Novikov cohomology for the complement of a hyperplane arrangement vanishes except in the middle dimensi...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(C))
Project Year: 2007 - 2009    Investigator(s): Hidehiko KAMIYA
We solved some problems about rankings by using the theory of hyperplane arrangements. In the course of the argument, we also generalized a method in the arrangement theory. Specifically, we found the number of ranking patterns generated by the un...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(C))
Project Year: 2006 - 2008    Investigator(s): Toru NAKASHIMA
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(A))
Project Year: 2006 - 2008    Investigator(s): Guest MARTIN
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 2005 - 2008    Investigator(s): Hiroaki TERAO
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 2004 - 2007    Investigator(s): Kyoji SAITO
The subject of the present research program is the Lie theoretic study of primitive forms and their period maps. We obtain several results, which are briefly summarized as follows.1. In a series of joint works with H. Kajiura and A. Takahashi, we ...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 2004 - 2007    Investigator(s): Toshitake KOHNO
1. Loop spaces of orbit configuration spaces}In collaboration with F.Cohen and M.Xiconténcatl, I developed research on the algebraic structure of the homology of loop spaces of configuration spaces. We described the homology of loop spaces of or...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 2004 - 2006    Investigator(s): Mutsuo OKA
We did a systematic research on the singularity theory of plane curves, Fundamental groups of the Complements, Zariski Pairs, Alexander polynomials and its generalization, theta-Alexander polynomials.This generalization plays an important role for...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 2002 - 2004    Investigator(s): Hiroaki THRAO
1. In "Moduli space of combinatorially equivalent arrangements of hyperplanes and logarithmic Gauss-Manin connections."(H.Terao), we scrutinized the structure of the boundary divisor of the moduli space of hyperplane arrangements with a fixed numb...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(C))
Project Year: 2001 - 2003    Investigator(s): Takeshi KAWASAKI
Let A be a Noetherian ring and I an ideal of A. If I is of positive height and the Rees algebra R(I) of I is Cohen-Macaulay, then R(I) is called an Arithmetic Cohen-Macaulayfication of A. We give a necessary and sufficient condition for A to have ...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 2001 - 2003    Investigator(s): Kyoji SAITO
The main purpose of the present research program is to describe the period map associated to an integral of a primitive form in terms of Lie theory.I. Subject related to elliptic Lie algebra and elliptic Lie groups.1. The construction of the highe...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(C))
Project Year: 2000 - 2002    Investigator(s): Kazuhiko KURANO
1. We proved that the positivity problem of intersection multiplicity had a deep relation with the positivity of Dutta multiplicity. The Dutta multiplicity of a complex is a rational number that was defined by Dutta in the case of positive charact...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 1999 - 2001    Investigator(s): Hiroaki TERAO
In the 2001 fiscal year, we obtained the following two major research results :1. We showed that there exists a canonical basis for the module of vector fields tangent to a Coveter arrangement in a multiple order. We also showed the basis has deep...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(C))
Project Year: 1998 - 1999    Investigator(s): ト部 東介, Kazuhiko KURANO
Our aim was to make resolution of singularities in arbitrary characteristic (or, more generally, in mixed-characteristic). By the help of the fund, investigators have got various results around the problem. Kurano described localized Chern charact...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 1998 - 1999    Investigator(s): Ken NAKAMULA
The objects of this study are to compute invariants on elementary number theory, algebraic number fields and elliptic curves computers using already known theorems and methods, then to gain realistic accumulation of data and to establish theoretic...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 1997 - 1999    Investigator(s): Mutsuo OKA
In this research, we tried to proceed a systematical study for Singularity theory, with a special viewpoint from fundamental group.M. Oka, H. Tokunaga and I. Shimada studied the fundamental groups of the complement of plane curves with singulariti...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(C))
Project Year: 1997 - 1998    Investigator(s): Hirofumi YAMADA
I focused on a relationship of Schur's Q-functions and affine Lie algebras. First I found that the Q-functions, expressed as polynomials of power sum symmetric functions, form a weight basis for the basic representation of certain affine Lie algeb...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 1997 - 1998    Investigator(s): 寺尾 宏明, Yuichiro TAKEDA
(1)The following result was obtained concerning hyperplane arrangements which are naturally determined by reflection groups : the modules of vector fields which are doubly tangent to the hyperplane arrangements have free bases (Solomon Terao). Thi...
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(総合研究(A), 基盤研究(A))
Project Year: 1995 - 1996    Investigator(s): Nobuo SASAKURA
First of all Nobuo Sasahuca made progresses on his proposed theoy of construction of sheaee. He initrated sone basic formla for rank tro sheares formed arithmetically. Also he found a rank a bandle or II_4, which leads to discovery of elliptic con...