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]
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...
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...
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...
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...
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...
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...
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...
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 \...
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]
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 ...
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...
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 ...
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
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...
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...
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 ...
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...
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...
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 ...
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...
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...
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...
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...
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...
(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...
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...
