2018年度

第10回

  • 日時:2019年3月1日(金) 17:30~18:30, 18:45~19:45
  • 場所:I-siteなんば 2F S1 (I-siteなんばへは，地下鉄御堂筋線大国町駅が最寄りです．)
  • 講演者:榎園誠氏(大阪大学)
  • タイトル:The cohomology rings of regular nilpotent Hessenberg varieties
  • アブストラクト: Hessenberg varieties are subvarieties of the full flag variety, which were introduced by De Mari-Procesi-Shayman around 1990. They has been studied in many areas of mathematics: algebraic geometry, representation theory, combinatorics and so on. In this talk, I will discuss the cohomology rings of regular nilpotent Hessenberg varieties in all Lie types. In particular, I want to explain generators of the defining ideals and an additive basis of their cohomology rings in terms of the root system. This is joint work with Takahiro Nagaoka, Tatsuya Horiguchi and Akiyoshi Tsuchiya.

第9回

  • 日時: 2019年1月25日(金) 17:30~18:30, 18:45~19:45
  • 場所:I-siteなんば 2F S1 (I-siteなんばへは，地下鉄御堂筋線大国町駅が最寄りです．)
  • 講演者:川谷康太郎氏(大阪大学)
  • タイトル:Stability conditions on morphisms on a category
  • アブストラクト:Let D be a triangulated category. If the space Stab(D) of stability conditions on D is not empty, each connected component of Stab(D) is a complex manifold due to Bridgeland. Let M be the category of morphisms in the category D. If D has an appropriate enhancement then M is also triangulated. In particular the space Stab(M) of stability conditions on M is well defined. Basic motivation is the comparison of Stab(D) and Stab(M). In this talk, I will explain some fundamental results for the comparison after a brief introduction of the backgrounds.

第8回

  • 日時:2018年12月14日(金) 17:30~18:30, 18:45~19:45
  • 場所: I-siteなんば 2F S1 (I-siteなんばへは，地下鉄御堂筋線大国町駅が最寄りです．)
  • 講演者: 藤田直樹氏(東京工業大学)
  • タイトル: Nakashima-Zelevinsky polytopes from convex-geometric Demazure operators
  • アブストラクト: A Nakashima-Zelevinsky polytope is a rational convex polytope whose lattice points give a polyhedral realization of a highest weight crystal basis. This is also identical to a Newton-Okounkov body of a flag variety, and it induces a toric degeneration. In this talk, we give a new construction of a specific class of Nakashima-Zelevinsky polytopes by using Kiritchenko's Demazure operators on polytopes. From this construction, we see that polytopes in this class have the additivity with respect to the Minkowski sum. We also give a geometric application to the normal toric variety associated with a Nakashima-Zelevinsky polytope.

第7回

  • 日時:2018年11月28日(水) 14:45~18:00
  • 場所:大阪府立大学 A13-405 (建物が普段と異なるのでご注意下さい)
  • 講演者:宮本 賢伍氏(大阪大学)
  • タイトル:On Auslander-Reiten Heller components for symmetric orders
  • アブストラクト:The notion of almost split sequences was introduced by M. Auslander and I. Reiten around 1970, and they showed the existence of almost split sequences for Artin algebras. We often use the theory to analyze various additive categories arising from representation theory and prove many important combinatorial and homological properties with the help of the theory. A combinatorial skeleton of the additive category of indecomposable objects is the Auslander–Reiten quiver, which encapsulates much information on indecomposable objects and irreducible morphisms. Therefore, to determine the shapes of Auslander–Reiten quivers is one of classical problems in representation theory of algebras. For a symmetric order over a complete discrete valuation ring, the stable Auslandr-Reiten quiver is obtained by deleting proj-inj vertices from the Auslander-Reiten quiver. When the order is not an isolated singularity, the shapes of the stable Auslander-Reiten components are mostly unknown. In this talk, we will give a restriction on the shapes of the stable Auslander-Reiten components and give examples of the stable Auslander-Reiten components by focusing on Heller lattices.

第6回

  • 日時: 2018年11月20日(火) 17:30~18:30, 18:45~19:45
  • 場所: I-siteなんば 2F S1 (I-siteなんばへは，地下鉄御堂筋線大国町駅が最寄りです。)
  • 講演者: 水野有哉氏(静岡大学)
  • タイトル: Preprojective algebras of Dynkin type and two-sided tilting complexes
  • アブストラクト: In this talk, we discuss tilting theory of preprojective algebras of Dynkin type. In the case of non-Dynkin type, we can give a simple and explicit description of two-sided tilting complexes, which provide auto-equivalences of the derived categories. On the other hand, in the case of Dynkin type, tilting theory is more involved and such a description hasn't been discovered. In this talk, we discuss tilting theory of preprojective algebras of Dynkin type and explain a construction of two-sided tilting complexes.

第5回

  • 日時: 2018年10月26日(金) 17:30~18:30, 18:45~19:45
  • 場所: I-siteなんば 2F S1
  • 講演者: 大矢浩徳氏(芝浦工業大学)
  • タイトル: Cluster realizations of Weyl groups and their application
  • アブストラクト: Cluster algebras are commutative algebras which are determined from combinatorial data represented by weighted quivers. These combinatorial data are used for successive construction, called mutation, of algebra generators. A cluster modular group is the group consisting of automorphisms of a cluster algebra which are given by mutation sequences preserving a given weighted quiver. In this talk, we realize the Weyl groups associated with symmetrizable Kac-Moody Lie algebras as subgroups of cluster modular groups. We explain application of our construction of Weyl groups : An algebraic application is a systematic construction of green sequences associated with reduced words of elements of the Weyl group. In particular, if a given Kac-Moody Lie algebra is of finite type, then reduced words of the longest element give the maximal green sequences (and the cluster Donaldson-Thomas transformation) associated to our weighted quiver. As a geometric application, we discuss the comparison between our realization of the Weyl group and a geometric action of the Weyl group on the moduli space of twisted decorated $G$-local systems on a marked surface, which is known to be a cluster variety. This talk is based on a joint work with Rei Inoue and Tsukasa Ishibashi.

第4回

  • 日時: 2018年7月27日 17:30~19:00, 19:15~20:15
  • 場所: I-siteなんば2F S1
  • 講演者:柴田大樹氏(岡山理科大学)
  • タイトル: On twisted loop groups and twisted affine Kac-Moody groups
  • アブストラクト: 無限次元カッツ・ムーディ代数の中でもよく理解されているアフィン・リー代数は，数学のみならず様々な分野に応用があり興味深い対象である．アフィン・リー代数のうちでtwisted なクラスは，untwisted なクラスに比べて見かけがだいぶ異なっている．しかしガロア・デサント理論の視点に立てば，twisted なものは適当なsplit のある種の固定点として理解でき非常に明快である．本講演ではアフィン・リー代数から構成される「アフィン型カッツ・ムーディ群」と呼ばれる抽象群もこれと同様の性質を持つことをいい，同時に代数的ループ群とも深く関連していることを紹介する．これは森田純氏（筑波大学）とArturo Pianzola氏（アルバータ大学）との共同研究である．

第3回

  • 場所: I-siteなんば 2F S1 (I-siteなんばへは，地下鉄御堂筋線大国町駅が最寄りです。)
  • タイトル：On bocses (survey)
  • 講演者:吉脇理雄氏(理化学研究所, 大阪市立大学数学研究所, 京都大学 高等研究院)
  • 日時: 2018年6月15日(金) 17:30~18:30, 18:45~19:45
  • アブストラクト:Crawley-Boeveyの論文をもとにbocs(a bimodule over a category with a coalgebra structure)に対する基本的な事項を紹介する。さらに「Tame and Wild Theorem（Drozd）」の証明における再定式化に用いられる layered bocs に着目して、それに関する操作であるreductionについてお話する。
  • 参考文献：

第2回

  • 日時: 2018年4月18日(水) 16:15-17:45
  • 場所: 大阪府立大学 なかもずキャンパス A14-321
  • 講演者: Martin Herschend氏 (Uppsala University)
  • Title: Algebras that admit n-cluster tilting subcategories
  • Abstract: In higher dimensional Auslander-Reiten theory one replaces the module category of an associative algebra by a subcategory with suitable homological properties. The most standard choice is to consider a so-called n-cluster tilting subcategory. A fundamental question is therefore: which algebras admit an n-cluster tilting subcategory of their module category? Although a definitive answer to this question seems to much to hope for, there are several results on how to obtain such algebras. In my talk I will give a survey of these results with a focus on algebras where an n-cluster tilting subcategory can be described explicitly.

第1回

  • 日時: 2018年4月2日 13:30~15:00, 15:30~17:00
  • 講演者: 長岡高広氏 (京都大学理学研究科)
  • 場所: I-siteなんば 2F S1 I-siteなんばへは，地下鉄御堂筋線大国町駅が最寄りです。
  • タイトル: The universal Poisson deformation space of hypertoric varieties and some classification results.
  • アブストラクト: Hypertoric variety $Y(A, \alpha)$ is a (holomorphic) symplectic variety, which is defined as Hamiltonian reduction of complex vector space by torus action. By definition, there exists projective morphism $\pi:Y(A, \alpha) \to Y(A, 0)$, and for generic $\alpha$, this gives a symplectic resolution of affine hypertoric variety $Y(A, 0)$. In general, for conical symplectic variety and it's symplectic resolution, Namikawa showed the existence of universal Poisson deformation space of them. We construct universal Poisson deformation space of hypertoric varieties $Y(A, \alpha)$, $Y(A, 0)$. We will explain this construction and concrete description of Namikawa-Weyl group action in this case. If time permits, We will also talk about some classification results of affine hypertoric variety. This talk is based on my master thesis.