Visitors of Algebraic Representation Theory Group in USTC

2021

• 12.9-1.8    Prof. Dr. Bernhard Keller (University of Paris)
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• Title: On extriangulated categories, exact infinity-categories and exact dg categories (I, II, III)
• Time: 12.17, 15:30-17:30 (I)
•          12.24, 15:30-17:30 (II)
•          1. 6, 10:00-12:00 (III)
• Location: GuanLiKeYan Building: Room 1318 (I,II), Room 1208 (III)
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• Abstract:In this lecture series, we will present recent developments concerning the three generalizations of Quillen's notion of exact category mentioned in the title.
•    In the first lecture, we will introduce extriangulated categories following the work of Nakaoka-Palu (2019). This notion generalizes both, the notion of exact and that of triangulated category. It arises naturally in the categorification of cluster algebras with coefficients. Here the relevant categories are due to Pressland (for many examples) and Yilin Wu (in full generality).
•    The second lecture will be devoted to infinity-categories (modeled using quasi-categories)and more specifically to exact infinity-categories in the sense of Barwick (2015 and 2016).The link to extriangulated categories is given by Nakaoka-Palu's theorem (04/2020) stating that the homotopy category of an exact infinity-category carries a canonical extriangulated structure. Such extriangulated categories are called *topological* extriangulated categories.
•    The third lecture is motivated by the search for a suitable notion of *algebraic* extriangulated category, i.e. a class of differential graded (=dg) k-categories whose H^0 carries a natural extriangulated structure in analogy of with that of topological extriangulated categories.We will present the solution proposed by Xiaofa Chen in his ongoing Ph. D thesis. It seems very likely that Lurie's dg nerve functor transforms an exact dg category in the sense of Chen into an exact infinity-category in the sense of Barwick and that the exact infinity-categories obtained in this way are precisely those admitting a k-linear structure. (One can get the slides here.)
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• 11.12    Prof. Dr. Shiquan Ruan (Xiamen University) Online
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• Title: Nakayama algebras and Fuchsian singularities
• Time: 11.12, 15:00-16:30
• Tencent number: 260 499 054
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• Abstract: In this talk, we will consider an important class of Nakayama algebras $N_n(r)$ given by the path algebras of the equioriented quiver $A_n$ subject to the nilpotency degree $r$ for each sequence of $r$ consecutive arrows. We classify all the Nakayama algebras $N_n(r)$ having Fuchsian type, that is, derived equivalent to the extended canonical algebras. As a byproduct, we reprove the Nakayama algebras of piecewise hereditary type, which have been classified by Happel-Seidel earlier. This is joint work with Helmut Lenzing and Hagen Meltzer.
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• 7.21-7.23    Prof. Dr. Ming Lu (Sichuan University)
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• Title: Hall algebra of the projective line and q-Onsager algebra
• Time: 7.22, 15:30-17:00
• Location: GuanLiKeYan Building, Room 1318
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• Abstract: A quantum symmetric pair consists of a quantum group and its coideal subalgebra (called an i-quantum group). A quantum group can be viewed as an example of i-quantum groups associated to symmetric pairs of diagonal type.
•    Recently, we present a geometric construction of affine i-quantum groups in Drinfeld type presentation. For simplicity, in this talk, we mainly focus on the i-quantum group of type affine sl_2, which is also called q-Onsager algebra. The Drinfeld type presentation of the q-Onsager algebra is introduced, and it can be realized by using the i-Hall algebra of the projective line. This is joint work with Shiquan Ruan and Weiqiang Wang.
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• 5.17    Prof. Dr. Guodong Zhou (East China Normal University) Online
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• Title: Algebraic Morse theory via homological perturbation lemma with applications to Chinese algebras
• Time: 5.17, 14:45-16:45
• Tencent number: 763 328 715
• Password: 210517
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• Abstract: As a generalization of the classical killing-contractible-complex lemma, we present algebraic Morse theory via homological perturbation theory, in a form more general than existing presentations in the literature. We also give a criterion for the two-sided Anick resolution to be a minimal resolution. At last, we apply algebraic Morse theory to Chinese algebras and show that a Chinese algebras of rank $n$ is homologically smooth and of global dimension $\frac{n(n+1)}{2}$.
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• 4.16    Prof. Dr. Shengfei Geng (Sichuan University) Online
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• Title: Tilting modules and support $\tau$-tilting modules over preprojective algebras associated with symmetrizable Cartan matrices
• Time: 4.16, 15:00-17:00
• Zoom number: 9739747578
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• Abstract: For any given symmetrizable Cartan matrix $C$ with a symmetrizer $D$, Geiss-Leclerc-Schr\{o}er (Invent. Math. 209, 61-158 (2017)) introduced a generalized preprojective algebra $\Pi(C, D)$. We study tilting modules and support $\tau$-tilting modules for the generalized preprojective algebra $\Pi(C, D)$ and show that there is a bijection between the set of all cofinite tilting ideals of $\Pi(C,D)$ and the corresponding Weyl group $W(C)$ provided that $C$ has no component of Dynkin type. When $C$ is of Dynkin type, we also establish a bijection between the set of all basic support $\tau$-tilting $\Pi(C,D)$-modules and the corresponding Weyl group $W(C)$. These results generalize the classification results of Buan et al. (Compos. Math. 145(4), 1035–1079 (2009)) and Mizuno (Math. Zeit. 277(3), 665–690 (2014)) over classical preprojective algebras. This talk is based on joint work with Changjian Fu.
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• 4.2    Prof. Dr. Zhaobing Fan (Harbin Engineering University)
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• Title: Drinfeld double of deformed quantum algebras
• Time: 4.2, 10:45-11:45
• Location: GuanLiKeYan Building, Room 1418
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• Abstract: We provide a deformation, f_{\alpha, \beta} , of Lusztig algebra f. Various quantum algebras in literature, including half parts of two-parameter quantum algebras, quantum superalgebras, and multi-parameter quantum algebras/superalgebras, are all specializations of f_{\alpha, \beta} . Moreover, f_{\alpha, \beta} is isomorphic to Lusztig algebra f up to a twist. As a consequence, half parts of those quantum algebras are isomorphic to Lusztig algebra f over a big enough ground field up to certain twists. We further construct the entire algebra U _{\beta, \xi} by Drinfeld double construction. As special cases, above quantum algebras all admit a Drinfeld double construction under certain assumptions. This is a joint work with Junjing Xing.
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• 1.30 & 2.1 & 2.3    Prof. Dr. Fei Xu (Shantou University) Online
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• Title: p-模系统简介 (I, II, III)
• Time: 1.30, 14:00-15:30 (I)
•           2.1, 14:00-16:00 (II)  
•           2.3, 14:00-17:00 (III)  
• Zoom number: 9739747578
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• 摘要: p-模系统是群表示理论里的经典内容，特别是在特征零域上的表示到特征p域上的表示的约化理论中扮演重要角色。(笔记在这里.)
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• 1.18 - 1.29   Junyang Liu (Tsinghua University)
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• 12.21-1.29    Prof. Dr. Bernhard Keller (University of Paris)
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• Title: Higher preprojective algebras via Calabi-Yau completions (I, II, III, IV)
• Time: 1. 8, 10:00-12:00 (I)
•          1.18, 15:00-17:00 (II)
•          1.22, 15:00-17:00 (III)
•          1.25, 10:00-12:00 (IV)
• Location: GuanLiKeYan Building, Room 1318
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• Abstract: In 2013, Iyama and Oppermann introduced higher preprojective algebras associated with n-representation finite algebras and showed that they enjoy properties analogous to those of preprojective algbras of Dynkin quivers. We will show how these properties follow easily from those of Calabi-Yau completions. (One can get the slides here.)
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• 12.27-1.9    Dr. Peigen Cao (Zhejiang University)
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• Title: d-compatibility degree of cluster algebras
• Time: 1.7, 16:00-17:30
Location: GuanLiKeYan Building, Room 1318
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• Abstract: In this talk, we will talk about some properties of d-compatibility degree of cluster algebras. We will use some combinatorial information on a hexagon to analogize the combinations of cluster algebras, and use the number of crossings between two diagonals of the hexagon to analogize the d-compatibility degree of cluster algebras. This talk is based on a joint work with Professor Fang Li.
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2020

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• 12.26 - 29   Prof. Dr. Yu Qiu (Tsinghua University)
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• Title: Topological realization of Lagrangian immersions
• Time: 12.26, 16:00-17:00
Location: GuanLiKeYan Building, Room 1318
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• Abstract: We discuss the relations between various Calabi-Yau categories of gentle type and their topological realizations. This is a joint work with Ikeda and Zhou.
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• 12.24 - 1.9    Yu Wang (Nanjing University)
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• 12.21 - 1.13   Junyang Liu (Tsinghua University)
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• Previous visitors see here recorded by Xiao-Wu Chen.
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