TAKURO ABE | Last modified date：2020.03.04 |

Professor /
Division of Fundamental mathematics /
Institute of Mathematics for Industry

**Presentations**

1. | 阿部拓郎, Free arrangements, combinatorics and geometry, Hyperplane Arrangements and Singularities, 2019.12, [URL], 超平面配置とは超平面の有限集合であり、それが自由であるとは対応する対数的ベクトル場が自由加群となる場合に言う。 寺尾の分解定理より、自由性は補空間の位相幾何や組合せ論と関連させら手織り、超平面配置研究の中心的話題の一つである。 関連する寺尾予想は、自由星の組み合わせ依存性を主張している40年来の未解決問題であるが、いまだ本質的な進展は少ない。 本講演では寺尾予想及び自由配置に関連した、近年の講演者らを中心とする進展及び今後の展望を概説する。. |

2. | 阿部拓郎, Free arrangements, restrictions and related topics, Hyperplane Arrangements and Reflection Groups, 2019.09, [URL]. |

3. | Takuro Abe, Solomon-Terao algebra of hyperplane arrangements and singularities, Special Session on Geometry and Topology of Singularities, 2019.09, [URL]. |

4. | 阿部拓郎, Recent topics on free arrangements, Arrangements at Western, 2019.05, [URL]. |

5. | 阿部拓郎, Combinatorics of the addition-deletion theorems for free arrangements, CIMPA - IMH Research School HYPERPLANE ARRANGEMENTS: RECENT ADVANCES AND OPEN PROBLEMS, 2019.03, [URL]. |

6. | 阿部拓郎, Combinatorics of the addition-deletion theorems for arrangements, On hyperplane arrangements, configuration spaces and related topics, 2019.02, [URL]. |

7. | 阿部拓郎, Logarithmic vector fields and freeness of hyperplane arrangements, Free divisors and Hyperplane arrangements, 2018.12, [URL]. |

8. | 阿部拓郎, Hessenberg varieties and hyperplane arrangements, Hessenberg varieties 2018 in Osaka, 2018.12, [URL]. |

9. | , [URL]. |

10. | 阿部拓郎, Hessenbergs and hyperplane arrangements part II, Hessenberg Varieties in Combinatorics, Geometry and Representation Theory, 2018.10. |

11. | , [URL]. |

12. | 阿部拓郎, The b_2-equality and free arrangements, New perspectives in hyperplane arrangements, 2018.09, [URL]. |

13. | 阿部拓郎, Free arrangements of hyperplanes and applications, Workshop on Algebraic Geometry, 2018.06. |

14. | Takuro Abe, Generators for logarithmic derivation modules of hyperplane arrangements, Topology and Geometry: A conference in memory of Stefan Papadima (1953-2018), 2018.05, [URL], The most famous nice generators for logarithmic derivation modules of arrangements are free bases when the arrangement is free. Dimca and Sticlaru introduced a nearly free plane curves, which has also a nice set of generators. We study more on a set of nice generators.. |

15. | Takuro Abe, Generators of logarithmic derivation modules of hyperplane arrangements, Arrangements of Hypersurfaces, 2018.04, [URL], Logarithmic derivation modules are one of the most important objects to study in of hyperplane arrangements and hypersurfaces. In particular, the freeness of them have been intensively studied. But in general they are not free. By Dimca and Sticlaru, the near freeness of plane curves and cubic surfaces are introduced, which is close to the freeness from the viewpoint of the number of generators. We study several properties of free and nearly free curves from algebro- geometric points of view, and consider the higher dimensional version of them. This talk contains a joint work with Alex Dimca.. |

16. | 阿部拓郎, Poincare polynomials and free arrangements, A walk between hyperplane arrangements, computer algebra and algorithms, 2018.02. |

17. | 阿部拓郎, Solomon-Terao algebra of hyperplane arrangements, Topology of arrangements and representation stability, 2018.01. |

18. | 阿部拓郎, Solomon-Terao algebra of hyperplane arrangements, Toric Topology 2017 in Osaka, 2017.12. |

19. | 阿部 拓郎, Hyperplane arrangements and Hessenberg varieties, The 5th Franco-Japan-Vietnamese Symposium on Singularities, 2017.11. |

20. | 阿部 拓郎, Freeness and combinatorics of hyperplane arrangements, Seminaires de Mathematiques et de leurs Applications, 2017.09. |

21. | 阿部 拓郎, Free arrangements and vector bundles, VIIIe rencontre Pau-Zaragoza d'Algebra et Geometrie, 2017.09. |

22. | 阿部 拓郎, The b2-inequality and freeness of the restrictions of hyperplane arrangements, Advances in Hyperplane Arrangements, 2017.08. |

23. | 阿部 拓郎, Hyperplane arrangements and Hessenberg varieties, Advances in Arrangement Theory, Mathematical Congress of the Americas, 2017.07, イデアル配置から構成されるSolomon-寺尾代数と、同じイデアルから構成される正則冪零Hessenberg多様体のコホモロジー環が同型となることを示した。. |

24. | 阿部 拓郎, Hyperplane arrangements and Hessenberg varieties, Arrangements and beyond, 2017.06, [URL], Hessenberg varieties were introduced by De Mari, Procesi and Shayman as a generalization of flag varieties. Recently, for the regular nilpotent and regular semisimple cases, their topologies are intensively studied, and related to combinatorial and (geometric) representational aspects. However, the algebraic structure of their cohomology groups have been unknown except for the case of type A. Recalling the fact that their cohomology rings are isomorphic to the coinvariant algebras, and Kyoji Saito's original proof of the freeness of Weyl arrangements by using basic invariants, we give a presentation of the cohomology group of a regular nilpotent Hessenberg variety by using a logarithmic derivation module of certain hyperplane arrangements (ideal arrangements) coming from the Hessenberg variety. Also, several properties of cohomology groups like complete intersection, hard Lefschetz properties and Hodge-Riemann relations are shown.. |

25. | 阿部 拓郎, Hyperplane arrangments, Solomon-Terao algebras and applications to Hessenberg varieties, 変換群を核とする代数的位相幾何学, 2017.05. |

26. | 阿部 拓郎, Algebra and geometry of Solomon-Terao's formula, Hyperplane Arrangements and related topics, 2017.02. |

27. | 阿部 拓郎, Algebra and combinatorics of hyperplane arrangements, The 15th Japan-Korea Workshop on Algebra and Combinatorics, 2017.02. |

28. | 阿部 拓郎, Hyperplane arrangements and Hessenberg varieties, Oberseminar, 2016.12. |

29. | , [URL]. |

30. | 阿部 拓郎, Recent developments on algebra of line arrangements, The 2nd Franco-Japanese-Vietnamese Symposium on Singularities, 2015.08, [URL]. |

31. | 阿部 拓郎, Division and localization of characteristic polynomials of hyperplane arrangements, Combinatorics and Algebraic Topology of Configurations, 2015.02, [URL]. |

32. | 阿部 拓郎, Division free theorem for line arrangements and divisionally free arrangements of hyperplanes, Arrangements of plane curves and related problems, 2015.03, [URL]. |

33. | 阿部 拓郎, Divisional freeness and the second Betti number of hyperplane arrangements, Hyperplane arrangements and reflection groups, 2015.08, [URL]. |

34. | 阿部 拓郎, Divisional freeness and the second Betti number of hyperplane arrangements, Differential and combinatorial aspects of singularities, 2015.08, [URL]. |

35. | 阿部 拓郎, Recent topics on free arrangements of hyperplanes, Summer Conference on Hyperplane Arrangements(SCHA) in Sapporo, 2016.08, [URL], Freeness has been one of the central topics among the theory of hyperplane arrangements. There are several important results like Terao's addition-deletion and factorization therems, the moduli theoretic approach by Yusvinsky and so on. In particular, Yoshinaga's criterion on freeness by using mutliarrangemens gave a breakthrough in this study area, and there have been a lot of new approaches on freeness problem. In this talk, we discuss several recent results including freeness criterion, multiple addition theorems and divisional freeness. Also, we discuss the new algebraic class of line arramgenents and plane curves in the projective plane called near freeness by Dimca and Sticlaru. Moreover, we pose some problems which appeared in this ten years.. |

36. | 阿部 拓郎, Divisionally free arrangements of hyperplanes , MS seminar, 2016.06, Abstract: Free arrangements of hyperplanes were introduced by K. Saito in 1970's. There are a lot of ways to understand free arrangements, but one of them is a generalization of Weyl arrangements and groups in terms of their exponents, i.e., by using loga. |

37. | 阿部 拓郎, Divisional flags and freeness of hyperplane arrangements, The JapaneseConference on Combinatorics and its Applications, Mini symposium:Combinatorics of hyperplane arrangements, 2016.05. |

38. | 阿部 拓郎, Some remarks on nearly free arrangements of lines in the projective plane, Workshop on Hyperplane Arrangements and Singularity Theory, 2016.03. |

39. | 阿部 拓郎, Freeness and flags of hyperplane arrangements, Special Session on Topology and Combinatorics of Arrangements (in honor of Mike Falk), AMS Sectional Meeting, 2016.03. |

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