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Higashitani Akihiro

東谷 章弘

Graduate School of Information Science and Technology Department of Pure and Applied Mathematics, Associate Professor

Education

  • 2009/04 - 2012/09, Osaka University, Graduate School of Information Science of Technology, Department of Pure and Applied Mathematics
  • 2005/04 - 2009/03, Osaka University, Faculty of Science, Department of Mathematics

Research History

  • 2019/04 - Present, Osaka University, Graduate School of Information Science and Technology, Department of Pure and Applied Mathematcs, Assoiate Professor
  • 2017/04 - 2019/03, Kyoto Sangyo University, Faculty of Science, Department of Mathematics, Assoiate Professor
  • 2015/04 - 2017/03, Kyoto Sangyo University, Faculty of Science, Department of Mathematics, Assistant Professor
  • 2014/04 - 2015/03, Kyoto University, Graduate School of Science, Department of Mathematcs, Postdoctoral Fellow (SPD)
  • 2012/10 - 2014/03, Osaka University, Graduate School of Information Science and Technology, Department of Pure and Applied Mathematcs, Postdoctoral Fellow (PD)

Research Areas

  • Natural sciences, Algebra

Professional Memberships

  • 日本数学会

Papers

  • Generalized F-signatures of Hibi rings, Akihiro Higashitani,Yusuke Nakajima, Illinois J. Math., Vol. 65, No. 1, p. 97-120, 2021/04
  • Winding Number of r-modular sequences and Applications to the Singularity Content of a Fano Polygon, Daniel Cavey,Akihiro Higashitani, Tohoku Math. J., Vol. 73, No. 1, p. 137-158, 2021/03
  • Combinatorial study of stable categories of graded Cohen-Macauly modules over skew quadric hypersufaces, Akihiro Higashitani,Kenta Ueyama, Collect. Math., 2021/02
  • Quadratic Gr\"obner bases of block diagonal matching field ideals and toric degenerations of Grassmannians, Akihiro Higashitani,Hidefumi Ohsugi, J. Pure Appl. Algebra, 2021
  • Combinatorial Mutations and Block Diagonal Polytopes, Oliver Clarke,Akihiro Higashitani,Fatemeh Mohammadi, Collect. Math., to appear., 2021
  • Cohomological rigidity for toric Fano manifolds of small dimensions or large Picard numbers, Akihiro Higashitani,Kazuki Kurimoto,Mikiya Masuda, Osaka Journal of Mathematics, to appear., 2021
  • Universal conditions on h*-vectors of lattice simplices, Akihiro Higashitani, Journal of Geometry, Vol. 112, No. 1, p. 1-9, 2021/01
  • Newton-Okounkov bodies of flag varieties and combinatorial mutations, Naoki Fujita,Akihiro Higashitani, Int. Math. Res. Not., to appear, 2020/10
  • Gorenstein polytopes with trinomial $h^*$-polynomials, Akihiro Higashitani,Benjamin Nill,Akiyoshi Tsuchiya, Beiträge zur Algebra und Geometrie, to appear, 2020
  • Toric ideals of Minkowski sums of unit simplices, Akihiro Higashitani,Hidefumi Ohsugi, Algebraic Combinatorics, Vol. 3, No. 4, p. 831-837, 2020
  • Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions, Akihiro Higashitani,Yusuke Nakajima, Selecta Math. (N.S.), Vol. 25, No. 78, 2019/12
  • Distribution of accumulation points of roots for type (n-1,1) Coxeter groups, Akihiro Higashitani,Ryosuke Mineyama,Norihiro Nakashima, Nagoya Math. J., Vol. 235, p. 125-157, 2019/09
  • Smooth centrally symmetric polytopes in dimension 3 are IDP, Matthias Beck,Christian Haase,Akihiro Higashitani,Johannes Hofscheier,Katharina Jochemko,Lukas Katthän,Mateusz Michalek, Ann. Comb., Vol. 23, p. 255-262, 2019
  • Permutations with small maximal k-consecutive sums, Akihiro Higashitani,Kazuki Kurimoto, Discrete Math., Vol. 342, p. 2467-2481, 2019
  • Arithmetic Aspects of symmetric edge polytopes, Akihiro Higashitani,Katharina Jochemko,Mateusz Michalek, Mathematika, Vol. 65, p. 763-784, 2019
  • Unimodality on $\delta$-vectors of lattice polytopes and two related properties, Akihiro Higashitani, European J. Math., Vol. 5, No. 2, p. 333-355, 2019
  • Lattice simplices of maximal dimension with a given degree, Akihiro Higashitani, Michigan Math. J., Vol. 68, p. 193-210, 2019
  • Ehrhart Polynomial Roots of Reflexive Polytopes, Gabor Hegedus,Akihiro Higashitani,Alexander Kasprzyk, Electron. J. Combin., Vol. 26, p. 1-27, 2019
  • Ehrhart polynomials with negative coefficients, Takayuki Hibi,Akihiro Higashitani,Akiyoshi Tsuchiya,Koutarou Yoshida, Graphs and Comb., Vol. 35, p. 363-371, 2019
  • A necessary condition for an edge ring to satisfy Serre's condition $(S_2)$, Akihiro Higashitani,Kyouko Kimura, Advanced Studies in Pure Mathematics, Vol. 77, p. 121-128, 2018/08
  • Universal inequalities in Ehrhart Theory, Gabriele Balletti,Akihiro Higashitani, Israel J. Math., Vol. 227, p. 843-859, 2018
  • Existence of regular unimodular triangulations of dilated empty simplices, Takayuki Hibi,Akihiro Higashitani,Koutarou Yoshida, European J. Combin., Vol. 70, p. 374-383, 2018
  • Non-level semi-standard graded Cohen-Macaulay domain with h-vector (h(0), h(1), h(2)), Akihiro Higashitani,Kohji Yanagawa, JOURNAL OF PURE AND APPLIED ALGEBRA, ELSEVIER SCIENCE BV, Vol. 222, No. 1, p. 191-201, 2018/01
  • Lattice multipolygons, Akihiro Higashitani,Mikiya Masuda, KYOTO JOURNAL OF MATHEMATICS, DUKE UNIV PRESS, Vol. 57, No. 4, p. 807-828, 2017/12
  • Interlacing Ehrhart polynomials of reflexive polytopes, Akihiro Higashitani,Mario Kummer,Mateusz Michalek, SELECTA MATHEMATICA-NEW SERIES, SPRINGER BASEL AG, Vol. 23, No. 4, p. 2977-2998, 2017/10
  • Integer Decomposition Property of Free Sums of Convex Polytopes, Takayuki Hibi,Akihiro Higashitani, ANNALS OF COMBINATORICS, SPRINGER BASEL AG, Vol. 20, No. 3, p. 601-607, 2016/09
  • Minkowski sum of polytopes and its normality, Akihiro Higashitani, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, MATH SOC JAPAN, Vol. 68, No. 3, p. 1147-1159, 2016/07
  • Almost Gorenstein homogeneous rings and their h-vectors, Akihiro Higashitani, JOURNAL OF ALGEBRA, ACADEMIC PRESS INC ELSEVIER SCIENCE, Vol. 456, p. 190-206, 2016/06
  • Dominating induced matchings of finite graphs and regularity of edge ideals, Takayuki Hibi,Akihiro Higashitani,Kyouko Kimura,Akiyoshi Tsuchiya, JOURNAL OF ALGEBRAIC COMBINATORICS, SPRINGER, Vol. 43, No. 1, p. 173-198, 2016/02
  • Smooth Fano polytopes arising from finite directed graphs, Akihiro Higashitani, KYOTO JOURNAL OF MATHEMATICS, DUKE UNIV PRESS, Vol. 55, No. 3, p. 579-592, 2015/09
  • Algebraic study on Cameron-Walker graphs, Takayuki Hibi,Akihiro Higashitani,Kyouko Kimura,Augustine B. O'Keefe, JOURNAL OF ALGEBRA, ACADEMIC PRESS INC ELSEVIER SCIENCE, Vol. 422, p. 257-269, 2015/01
  • TORIC RINGS ARISING FROM CYCLIC POLYTOPES, Takayuki Hibi,Akihiro Higashitani,Lukas Katthaen,Ryota Okazaki, COMMUNICATIONS IN ALGEBRA, TAYLOR & FRANCIS INC, Vol. 43, No. 2, p. 778-794, 2015
  • Integer decomposition property of dilated polytopes, David A. Cox,Christian Haase,Takayuki Hibi,Akihiro Higashitani, ELECTRONIC JOURNAL OF COMBINATORICS, ELECTRONIC JOURNAL OF COMBINATORICS, Vol. 21, No. 4, p. 1-17, 2014/11
  • DEPTH OF INITIAL IDEALS OF NORMAL EDGE RINGS, Takayuki Hibi,Akihiro Higashitani,Kyouko Kimura,Augustine B. O'keefe, COMMUNICATIONS IN ALGEBRA, TAYLOR & FRANCIS INC, Vol. 42, No. 7, p. 2908-2922, 2014/07
  • Non-normal very ample polytopes and their holes, Akihiro Higashitani, ELECTRONIC JOURNAL OF COMBINATORICS, ELECTRONIC JOURNAL OF COMBINATORICS, Vol. 21, No. 1, p. 1-12, 2014/03
  • NORMAL CYCLIC POLYTOPES AND CYCLIC POLYTOPES THAT ARE NOT VERY AMPLE, Takayuki Hibi,Akihiro Higashitani,Lukas Katthaen,Ryota Okazaki, JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, CAMBRIDGE UNIV PRESS, Vol. 96, No. 1, p. 61-77, 2014/02
  • Ehrhart polynomials of integral simplices with prime volumes, Akihiro Higashitani, INTEGERS, Vol. 14, p. 1-15, 2014
  • Hermite normal forms and delta-vectors, Takayuki Hibi,Akihiro Higashitani,Nan Li, JOURNAL OF COMBINATORIAL THEORY SERIES A, ACADEMIC PRESS INC ELSEVIER SCIENCE, Vol. 119, No. 6, p. 1158-1173, 2012/08
  • Counterexamples of the Conjecture on Roots of Ehrhart Polynomials, Akihiro Higashitani, DISCRETE & COMPUTATIONAL GEOMETRY, SPRINGER, Vol. 47, No. 3, p. 618-623, 2012/04
  • Roots of Ehrhart polynomials arising from graphs, Tetsushi Matsui,Akihiro Higashitani,Yuuki Nagazawa,Hidefumi Ohsugi,Takayuki Hibi, JOURNAL OF ALGEBRAIC COMBINATORICS, SPRINGER, Vol. 34, No. 4, p. 721-749, 2011/12
  • DEPTH OF EDGE RINGS ARISING FROM FINITE GRAPHS, Takayuki Hibi,Akihiro Higashitani,Kyouko Kimura,Augustine B. O'Keefe, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, AMER MATHEMATICAL SOC, Vol. 139, No. 11, p. 3807-3813, 2011/11
  • ROOTS OF EHRHART POLYNOMIALS OF GORENSTEIN FANO POLYTOPES, Takayuki Hibi,Akihiro Higashitani,Hidefumi Ohsugi, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, AMER MATHEMATICAL SOC, Vol. 139, No. 10, p. 3727-3734, 2011/10
  • Smooth Fano Polytopes Arising from Finite Partially Ordered Sets, Takayuki Hibi,Akihiro Higashitani, DISCRETE & COMPUTATIONAL GEOMETRY, SPRINGER, Vol. 45, No. 3, p. 449-461, 2011/04
  • Ehrhart polynomials of convex polytopes with small volumes, Takayuki Hibi,Akihiro Higashitani,Yuuki Nagazawa, EUROPEAN JOURNAL OF COMBINATORICS, ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, Vol. 32, No. 2, p. 226-232, 2011/02
  • Shifted symmetric delta-vectors of convex polytopes, Akihiro Higashitani, DISCRETE MATHEMATICS, ELSEVIER SCIENCE BV, Vol. 310, No. 21, p. 2925-2934, 2010/11

Misc.

  • On the depth of edge rings, 日比 孝之,東谷 章弘,木村 杏子,Augustine,B. O'Keefe, 数理解析研究所講究録, Vol. 1769, p. 83-89, 2011/10/01

Publications

  • 鏡映の数学 -有限鏡映群の幾何学-, 小林雅人,陶山大輔,塚本靖之,中島規博,東谷章弘,嶺山良介, 丸善出版, 2015/08
  • グレブナー教室 -計算代数統計への招待-, 竹村彰道,日比孝之,原尚幸,東谷章弘,清智也,「グレブナー道場,著者一同,著,東谷は,章を担当, 共立出版, 2015/07

Awards

  • 日本数学会建部賢弘奨励賞, 日本数学会, 2012
  • Award of the Graduate School of Information Science and Technology of Osaka University, HIGASHITANI AKIHIRO, Osaka University, Graduate School of Information Science and Technology, 2011/03

Presentations

  • Block diagonal matching fieldイデアルとグラスマン多様体のトーリック退化, 東谷章弘,大杉英史, 日本数学会2021年度年会, 2021/03/15
  • 完全多部グラフのエッジ環のconic因子的イデアルと非可換クレパント特異点解消の構成, 東谷章弘,松下光虹, 日本数学会2021年度年会, 2021/03/15
  • Introduction to combinatorial mutations of polytopes and its applications, Akihiro Higashitani, Combinatorics on Flag Varieties and Related Topics 2021, 2021/01/27
  • Newton-Okounkov bodies of flag varieties and combinatorial mutations, Akihiro Higashitani, The McKay correspondence, mutation and related topics, 2020/08/14
  • Introduction to combinatorial mutation and its application, 東谷章弘, 代数・解析・幾何セミナー, 2020/02/12
  • Introduction to Stanley-Reisner ideals and its application to noncommutative algebraic geometry I, II, 東谷章弘, 第25回静岡代数学セミナー, 2019/12/13
  • Del Pezzo曲面の分類とFano凸多角形のsingularity content, 東谷 章弘, 日本数学会2019年度秋季分科会, 2019/09/20
  • トーリックFano多様体のコホモロジー剛性問題, 東谷 章弘, 日本数学会2019年度秋季分科会, 2019/09/20
  • Mutation of Fano polygons and singularity contents, 東谷 章弘, Special Geometry-Combinatorics seminar, 2019/08/08
  • Reflexive polytopes arising from finite graphs and the unimodality of $h^*$-vectors, 東谷 章弘, 第36回代数的組合せ論シンポジウム, 2019/06/18
  • Mutation of Fano polygons and singularity contents, 東谷 章弘, 大阪大学代数幾何学セミナー, 2019/04/22
  • Characterization problem on Ehrhart polynomials of lattice polytopes, 東谷 章弘, AlgebraGeometryCombinatorics Seminar, 2018/09/19
  • 高次元版ピックの公式について~エルハート理論への誘い~, 東谷 章弘, 北九州数理科学セミナー, 2018/07/20
  • Finding a new universal condition in Ehrhart theory, 東谷 章弘, Seminar "Facet of Complexity", 2018/07/05
  • 有限群の自己同型に付随するカンドルの構造について, 東谷 章弘, 変換群論における幾何・代数・組み合わせ論, 2018/06/07
  • 有限群の自己同型に付随するカンドルの構造について, 東谷 章弘, 広島大学トポロジー・幾何セミナー, 2018/05/30
  • Regular unimodular triangulations of dilated empty simplices and Grobner basis, 東谷 章弘, KTH Combinatorics Seminar, 2018/03/28
  • 膨らませた空単体の正則単模三角形分割の存在, 東谷 章弘, 日本数学会2018年度年会, 2018/03/21
  • 多項式環のSegre積のgeneralized F-signatureについて, 東谷 章弘, 日本数学会2018年度年会, 2018/03/21
  • 格子凸多面体のEhrhart多項式に関する研究の現代的潮流, 東谷 章弘, 第14回組合せ論若手研究集会, 2018/03/01
  • Characterization problem on Ehrhart polynomials of lattice polytopes, 東谷 章弘, Hakata Workshop: Winter Meeting 2018, 2018/02/23
  • Characterizations for the $h^*$-vectors of lattice polytopes, 東谷 章弘, Nonlinear Seminar in MPI, 2017/12/14
  • 円周上に並べた1からnの数のk連続和の最大値について, 東谷 章弘, COMAセミナー, 2017/11/10
  • Characterizations for the $h^*$-vectors of lattice polytopes, 東谷 章弘, Interactions with Lattice Polytopes, 2017/09/14
  • 格子の分類と整単体の分類, 東谷 章弘, 広島組合せ論セミナー, 2017/07/14
  • 格子多面体論のこれまでとこれから, 東谷 章弘, 日本数学会2017年度年会, 2017/03/26
  • 格子単体の分類と二元符号の分類の関係について, 東谷 章弘, 北九州ワークショップ「幾何学と組合せ論」, 2017/03/11
  • Lattice simplices of maximal dimension with a given degree, 東谷 章弘, Einstein Workshop on lattice polytopes, 2016/12/14
  • Characterization of lattice polytopes and family of subsets closed under symmetric difference, 東谷 章弘, 有限群・代数的組合せ論・頂点作用素代数の研究, 2016/12/05
  • Cayley decomposition for $(0,1)$-polytopes and its toric ideals, 東谷 章弘, Binomial Ideals and Algebraic Statistics, 2016/10/31
  • Level property on affine semigroup rings and their $h$-vectors, 東谷 章弘, Japan-Vietnam Workshop on Commutative Algebra 2016, 2016/09/21
  • Non-level semi-standard graded Cohen-Macaulay domains with $h$-vectors $(h_0, h_1, h_2)$, 東谷 章弘, 日本数学会2016年度秋季分科会, 2016/09/16
  • 次数が小さい整単体の分類, 東谷 章弘, 日本数学会2016年度秋季分科会, 2016/09/15
  • On counterexamples of Cayley conjecture for lattice simplices, 東谷 章弘, Conference on Commutative Algebra and Convex Polytopes, 2016/08/04
  • 整単体に付随する有限アーベル群と二元線型符号, 東谷 章弘, COMAセミナー, 2016/07/01
  • 整単体の分類と二元シンプレックス符号, 東谷 章弘, 東北大組合せ論セミナー, 2016/05/16
  • Equivalence classes for smooth Fano polytopes, 東谷 章弘, 九州代数幾何セミナー, 2016/04/27
  • 整単体の分類と二元シンプレックス符号, 東谷 章弘, 日本数学会2016年度年会, 2016/03/21
  • Almost Gorenstein標準的次数付き環とそのh列, 東谷 章弘, 日本数学会2016年度年会, 2016/03/21
  • 整凸多面体のEhrhart多項式と$\delta$列, 東谷 章弘, 山形大学セミナー, 2016/03/01
  • Almost Gorenstein homogeneous domains and their $h$-vectors, 東谷 章弘, Workshop on Commutative Algebra (Part II, Local algebra and Representation theory), 2016/01/05