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東京名古屋代数セミナー
過去の記録 ～05/21｜次回の予定｜今後の予定 05/22～
| 担当者 | 阿部 紀行、Aaron Chan、伊山 修、行田 康晃、淺井 聡太、高橋 亮 |
|---|---|
| セミナーURL | http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html |
過去の記録
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。
大川 領 氏 (神戸大学)
$(-2)$ blow-up formula (Japanese)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
オンライン開催の詳細は下記URLをご覧ください。
大川 領 氏 (神戸大学)
$(-2)$ 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 ]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。
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)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
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 ]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.
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。
松井 紘樹 氏 (東京大学)
Subcategories of module/derived categories and subsets of Zariski spectra (Japanese)
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
オンライン開催の詳細は下記URLをご覧ください。
松井 紘樹 氏 (東京大学)
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 ]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.
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。
平野 雄貴 氏 (京都大学)
Full strong exceptional collections for invertible polynomials of chain type
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
オンライン開催の詳細は下記URLをご覧ください。
平野 雄貴 氏 (京都大学)
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 ]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.
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。
酒井 嵐士 氏 (名古屋大学)
ICE-closed subcategories and wide tau-tilting modules (Japanese)
オンライン開催の詳細は上記URLをご覧ください。
酒井 嵐士 氏 (名古屋大学)
ICE-closed subcategories and wide tau-tilting modules (Japanese)
[ 講演概要 ]
多元環の表現論では、多元環上の加群のなす圏の部分圏が調べられてきた。例えば、torsion class やwide部分圏などがある。今回の講演ではこれら2つの共通の一般化であるアーベル圏のICE-closed 部分圏を紹介する。そしてICE-closed部分圏はwide 部分圏のtorsion classであることを見る。またsupport tau-tilting 加群の一般化であるwide tau-tilting 加群を導入し、ICE-closed 部分圏がwide tau-tilting 加群と対応することを見る。本講演の内容は榎本悠久氏との共同研究に基づいている。
多元環の表現論では、多元環上の加群のなす圏の部分圏が調べられてきた。例えば、torsion class やwide部分圏などがある。今回の講演ではこれら2つの共通の一般化であるアーベル圏のICE-closed 部分圏を紹介する。そしてICE-closed部分圏はwide 部分圏のtorsion classであることを見る。またsupport tau-tilting 加群の一般化であるwide tau-tilting 加群を導入し、ICE-closed 部分圏がwide tau-tilting 加群と対応することを見る。本講演の内容は榎本悠久氏との共同研究に基づいている。
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。
行田 康晃 氏 (名古屋大学)
Positive cluster complex and $\tau$-tilting complex (Japanese)
オンライン開催の詳細は上記URLをご覧ください。
行田 康晃 氏 (名古屋大学)
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.
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.
