東京名古屋代数セミナー

担当者 阿部 紀行、Aaron Chan、Erik Darpoe、伊山 修、中村 力、中岡 宏行、高橋 亮 http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

2021年02月24日(水)

16:00-17:30   オンライン開催
オンライン開催の詳細は下記URLをご覧ください。

[ 講演概要 ]

[ 講演参考URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

2021年02月10日(水)

16:00-17:30   オンライン開催
オンライン開催の詳細は下記URLをご覧ください。

Gentle代数の2重次数付きCalabi-Yau完備化と曲面の幾何学 (Japanese)
[ 講演概要 ]
Gentle代数は多元環の表現論において非常に重要な研究対象であるが, 近年, Haiden-Katzarkov-Kontsevich(HKK)は次数付きgentle代数の導来圏に対し, 曲面の(位相的)深谷圏との導来同値を与えた. この対応においては, 直既約加群と曲面上のあるクラスの弧の対応が与えられている.

この背景に基づき, この講演ではまず最初に次数付きgentle代数に付随した2重次数付きquiver with potential構成法を曲面の深谷圏から来る幾何学的アイディアに沿って説明し, そのGinzburg CY代数を用いて一般的なgentle代数のCY-X完備化の構成について説明をする. (Xは2重次数の中のコホモロジー的次数とは独立な方向の次数.)

この結果は, Yu Qiu氏, Yu Zhou氏との共同研究に基づく.
[ 講演参考URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

2021年01月21日(木)

17:00-18:30   オンライン開催
オンライン開催の詳細は下記URLをご覧ください。

Based modules over the i-quantum group of type AI (Japanese)
[ 講演概要 ]
In recent years, i-quantum groups are intensively studied because of their importance in various branches of mathematics and physics. Although i-quantum groups are thought of as generalizations of Drinfeld-Jimbo quantum groups, their representation theory is much more difficult than that of quantum groups. In this talk, I will focus on the i-quantum group of type AI. It is a non-standard quantization of the special orthogonal Lie algebra so_n. I will report my recent research on based modules, which are modules equipped with distinguished bases, called the i-canonical bases. The first main result is a new combinatorial formula describing the branching rule from sl_n to so_n. The second one is the irreducibility of cell modules associated with the i-canonical bases.
[ 講演参考URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

2021年01月14日(木)

16:00-17:30   オンライン開催
オンライン開催の詳細は下記URLをご覧ください。

$(-2)$ blow-up formula (Japanese)
[ 講演概要 ]
この講演では$A_1$特異点から定まるネクラソフ分配関数について紹介する. これは特異点解消上の枠付き連接層のモジュライにおける積分を係数とする母関数である. 特異点解消として二つ, 極小解消とスタック的な解消, つまり, 射影平面を位数$2$の巡回群で割った商スタックを考える. これら二つの特異点解消から定まるネクラソフ分配関数の関数等式について紹介する. ひとつは, 伊藤-丸吉-奥田が予想した関数等式であり, もうひとつを$(-2)$ blow-up formulaとして提案したい. 証明については細部を省略し, 望月拓郎氏による壁越え公式について基本的な例を使って紹介する。
[ 講演参考URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

2020年12月17日(木)

16:00-17:30   オンライン開催
オンライン開催の詳細は下記URLをご覧ください。
Xiao-Wu Chen 氏 (University of Science and Technology of China)
The finite EI categories of Cartan type (English)
[ 講演概要 ]
We will recall the notion of a finite free EI category introduced by Li. To each Cartan triple, we associate a finite free EI category, called the finite EI category of Cartan type. The corresponding category algebra is isomorphic to the 1-Gorenstein algebra, introduced by Geiss-Leclerc-Schroer, that is associated to possibly another Cartan triple. The construction of the second Cartan triple is related to the well-known unfolding of valued graphs. We will apply the obtained algebra isomorphism to re-interpret some tau-locally free modules as induced modules over a certain skew group algebra. This project is joint with Ren Wang.
[ 講演参考URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

2020年12月10日(木)

16:30-18:00   オンライン開催
オンライン開催の詳細は下記URLをご覧ください。

Subcategories of module/derived categories and subsets of Zariski spectra (Japanese)
[ 講演概要 ]
The classification problem of subcategories has been well considered in many areas. This problem is initiated by Gabriel in 1962 by giving a classification of localizing subcategories of the module category Mod R via specialization-closed subsets of the Zariski spectrum Spec R for a commutative noetherian ring. After that several authors tried to generalize this result in many ways. For example, four decades later, Krause introduced the notion of coherent subsets of Spec R and used it to classify wide subcategories of Mod R. In this talk, I will introduce the notions of n-wide subcategories of Mod R and n-coherent subsets of Spec R for a (possibly infinite) non-negative integer n. I will also introduce the notion of n-uniform subcategories of the derived category D(Mod R) and prove the correspondences among these classes. This result unifies/generalizes many known results such as the classification given by Gabriel, Krause, Neeman, Takahashi, Angeleri Hugel-Marks-Stovicek-Takahashi-Vitoria. This talk is based on joint work with Ryo Takahashi.
[ 講演参考URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

2020年12月03日(木)

16:00-17:30   オンライン開催
オンライン開催の詳細は下記URLをご覧ください。

Full strong exceptional collections for invertible polynomials of chain type
[ 講演概要 ]
Constructing a tilting object in the stable category of graded maximal Cohen-Macaulay modules over a given graded Gorenstein ring is an important problem in the representation theory of graded Gorenstein rings. For a hypersurface S/f in a graded regular ring S, this problem is equivalent to constructing a tilting object in the homotopy category of graded matrix factorizations of f. In this talk, we discuss this problem in the case when S is a polynomial ring, f is an invertible polynomial of chain type and S has a rank one abelian group grading (called the maximal grading of f), and in this case we show the existence of a tilting object arising from a full strong exceptional collection. This is a joint work with Genki Ouchi.
[ 講演参考URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

2020年11月12日(木)

16:00-17:30   オンライン開催
オンライン開催の詳細は上記URLをご覧ください。

ICE-closed subcategories and wide tau-tilting modules (Japanese)
[ 講演概要 ]

2020年10月27日(火)

16:30-18:00   オンライン開催
オンライン開催の詳細は上記URLをご覧ください。

Positive cluster complex and $\tau$-tilting complex (Japanese)
[ 講演概要 ]
In cluster algebra theory, cluster complexes are actively studied as simplicial complexes, which represent the structure of a seed and its mutations. In this talk, I will discuss a certain subcomplex, called positive cluster complex, of a cluster complex. This is a subcomplex whose vertex set consists of all cluster variables except for those in the initial seed. I will also introduce another simplicial complex in this talk - the tau-tilting complex, which has vertices given by all indecomposable tau-rigid modules, and simplices given by basic tau-rigid modules. In the case of a cluster-tilted algebra, it turns out that a tau-tilting complex corresponds to some positive cluster complex. Due to this fact, we can investigate the structure of a tau-tilting complex of tau-tilting finite type by using the tools of cluster algebra theory. This is joint work with Haruhisa Enomoto.