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学术会议
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| 2013年03月05日（开会日期：June 15-June 16, 2013）
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“未来十年中国数学教育展望”学术研讨会通知
由华东师范大学数学系主办的“未来十年中国数学教育展望”学术研讨会定于2013年6月15日至16日在上海华东师范大学召开。本研讨会的官方网站是http://math.ecnu.edu.cn/academia/sxjyzw。会议地点是华东师范大学普陀校区华申学术交流中心（上海市普陀区中山北路3663号新逸夫楼内）。
一、会议主题
本研讨会的主题是“未来十年中国数学教育展望”，主要目的是在深刻审视我国数学教育近年来发展变化的基础上，总结经验，发现问题，提出未来十年中国数学教育的发展目标和研究建设，促进我国数学教育的进一步发展和国际化进程。在会议期间，还将安排张奠宙老师八十寿辰的简短庆祝活动。
二、会议程序
本研讨会采取大会报告和分组报告的形式。
大会报告是30分钟的邀请报告，报告人是数学教育领域的知名学者，报告人姓名和报告题目将于2013年3月在研讨会的官方网站上予以公布。
分组报告每个约15分钟，与会者可自由提交论文，审查通过即可。分组报告的主题可围绕本学术研讨会的讨论文件展开，但不局限于此。该讨论文件将于2013年3月上传至本研讨论的官方网站。
三、报名注册
与会者可以到本研讨会的官方网站在线注册页注册。也下载注册单，填写完整后通过电子邮件发送给本研讨会注册专用邮件地址sxjyzw_ecnu@126.com报名。报名注册将于2013年3月开始。
注册费用为：正式代表600元/人，学生代表300元/人（需出示学生证）。
会议期间， 食宿自理。关于住宿和交通信息请参看本研讨会的官方网站。
四、联系人
鲍建生 jsbao@math.ecnu.edu.cn
吴颖康 ykwu@math.ecnu.edu.cn
干芸 1203957471@qq.com
孙婷 sun1989ting@qq.com
华东师范大学数学系
“未来十年中国数学教育展望”学术研讨会筹备组
2013-1-22
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| 2012年11月01日（开会日期：2012年11月6日至11月8日）
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第一届中俄最优控制和计算研讨会将于2012年11月6日至11月8日在上海举行。本次会议的主旨是为俄罗斯和上海市科研院所与高等学校的自动控制和计算领域的科学研究专家提供一个高水平的交流平台。研讨会上除了专题报告之外，还将对最优控制和计算的热点问题和俄罗斯科学界与上海地区科研院所和高等院校在相关领域深化合作与交流进行深入研讨。
参加本届研讨会的有来自俄罗斯的七位专家和复旦大学、上海交通大学、华东师范大学、同济大学、上海大学的十二位学者，中国计算数学学会理事长石钟慈院士出席会议。
本届会议由华东师范大学数学系承办。会议获得国家自然科学基金委员会和俄罗斯自然科学基金委员会联合资助，并得到上海市数学会和华东师范大学数学系资助。 |
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| 2012年10月12日（开会日期：2012年10月12日~10月14日）
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2012长三角代数会议
本次长三角代数会议将于2012年10月12日至14日在华东师范大学闵行校区举行。会议的目的是汇集江苏、浙江、安徽、上海四个地区从事代数学研究的专家、学者共同介绍、研讨他们的研究领域的新进展和新动向，并加强彼此之间的相互了解与合作。本次会议也是“上海代数日”系列研讨会的继续,第一届会议已于2010年11月在上海交通大学召开。我们希望能够及时地为华东地区的研究生和青年研究人员提供更多的机会，了解和掌握现代代数学领域中一些最前沿的工作和发展趋势。
本次会议得到数学系985项目和国家杰出青年基金资助。
组织委员会：
王建磐（主席）（华东师范大学）
秦厚荣（南京大学）
谈胜利（华东师范大学）
章璞（上海交通大学）
苏育才（同济大学）
芮和兵（华东师范大学）
会议时间地点：
2012年10月12日~10月14日 华东师范大学闵行校区数学楼102报告厅
会议用餐:
Breakfast Time:7:15 — 8:00 住教师之家的教师可在楼内二楼餐厅就餐
Lunch Time: 12:10 — 14:00 教师之家二楼餐厅（商务套餐）
Dinner Time: 18:00 教师之家二楼餐厅
10月13日晚餐宴请（Banquet）
本次会议报告人：
Yanhong Bao
(鲍炎红)
安徽大学
Huixiang Chen
(陈惠香)
扬州大学
Jianlong Chen
(陈建龙)
东南大学
Xiaowu Chen
(陈小伍)
中国科技大学
Qiang Fu
(付强)
同济大学
Naihong Hu
(胡乃红)
华东师范大学
Zhaoyong Huang
(黄兆泳)
南京大学
Cuibo Jiang
(姜翠波)
上海交通大学
Fang Li
(李方)
浙江大学
Gongxiang Liu
(刘公祥)
南京大学
Diming Lu
(卢涤明)
浙江大学
Claus Michael Ringel
上海交通大学
Yucai Su
(苏育才)
同济大学
Jiaqun Wei
(魏加群)
南京师范大学
Quanshui Wu
(吴泉水)
复旦大学
Xu Xu
(徐旭)
华东师范大学
Yu Ye
(叶郁)
中国科技大学
Pu Zhang
(章璞)
上海交通大学
Schedule of Talks
Venue: Math building 102 (数学系102报告厅)
Oct. 12-14
Oct 12
(Friday)
Oct 13
(Saturday)
Oct14
(Sunday)
8:45 – 9:00
Welcome Speech
9:00 – 9:50
C. M. Ringel
Quanshui Wu
Yucai Su
10:00 – 10:50
Qiang Fu
Diming Lu
Cuipo Jiang
10:50 – 11:10
Tea Break
11:10–12:00
Yu Ye
Yanhong Bao
Xu Xu
12:10 – 14:00
Lunch
14:30 – 15:20
Huixiang Chen
Fang Li
Naihong Hu
15:30 – 16:20
Gongxiang Liu
Xiaowu Chen
Jiaqun Wei
16:20 – 16:40
Tea Break
16:40 – 17:30
Zhaoyong Huang
Jianlong Chen
Pu Zhang
会议日程
12 Oct.
会议地点： 数学楼 102报告厅
Chairman：
8:45－9:00
Opening Ceremony
9:00 – 9:50
C. M. Ringel
Tubular triangulated categories
10:00 – 10:50
Qiang Fu
Quantum affine $\mathfrak{g}{{\mathfrak{l}}_{n}}$ and affine $q$-Schur algebras
10:50 – 11:10
Tea Break
11:10 – 12:00
Yu Ye
Filtered module categories and related homological conjectures
12:10 – 14:30
Lunch
14:30 – 15:20
Huixiang Chen
The Coalgebra Automorphism Group of Hopf algebra ${{k}_{q}}[x,{{x}^{-1}},y]$
15:30 – 16:20
Gongxiang Liu
Representation type of super cocommutative Hopf algebras
16:20 – 16:40
Tea Break
16:40 – 17:30
Zhaoyong Huang
The Construction of Proper Resolutions and Applications
13 Oct.
会议地点： 数学楼 102报告厅
Chairman：
9:00 – 9:50
Quanshui Wu
Calabi-Yau algebras and their homologies
10:00 – 10:50
Diming Lu
Progress on the classification of Artin-Schelter Regular Algebras
10:50 – 11:10
Tea Break
11:10 – 12:00
Yanhong Bao
Cohomology Theory for Poisson Algebras
12:10 – 14:30
Lunch
14:30 – 15:20
Fang Li
On the first Hochschild cohomology of admissible algebras and path algebras with oriented cycles
15:30 – 16:20
Xiaowu Chen
Leavitt path algebras and singularity categories
16:20 – 16:40
Tea Break
16:40 – 17:30
Jianlong Chen
Relative regularity and Drazin inverses
14 Oct.
会议地点： 数学楼 102报告厅
Chairman：
9:00 – 9:50
Yucai Su
Character and dimension formulas for queer Lie superalgebras
10:00 – 10:50
Cuipo Jiang
Representations of the vertex operator algebra $V_{{{L}_{2}}}^{{{A}_{4}}}$
10:50 – 11:10
Tea Break
11:10 – 12:00
Xu Xu
Decomposition matrices of cyclotomic NW and BMW algebras
12:10 – 14:30
Lunch
14:30 – 15:20
Naihong Hu
On finite- and infinite-dimensional representations of quantum groups of type A
15:30 – 16:20
Jiaqun Wei
Gorenstein homological theory for differential modules
16:20 – 16:40
Tea Break
16:40 – 17:30
Pu Zhang
Gorenstein-projective modules and symmetric recollements
Abstracts
Cohomology Theory for Poisson Algebras
Yanhong Bao
Department of Mathematics, Anhui University
baoyh@ahu.edu.cn
Abstract：In this talk, I will introduce the quasi-Poisson cohomology theory and Poisson cohomology theory for Poisson algebras. The relation between the formal deformation of Poisson algebras and the Poisson cohomology groups is also discussed. This is joint with Ye Yu.
The Coalgebra Automorphism Group of Hopf algebra ${{k}_{q}}[x,{{x}^{-1}},y]$
Huixiang Chen
Department of Mathematics, Yangzhou University
hxchen@yzu.edu.cn
Abstract：Let $k_q[x, x^{-1}, y]$ be the localization of the quantum plane $k_q[x, y]$ over a field $k$, where $0\neq q\in k$. Then $k_q[x, x^{-1}, y]$ is a graded Hopf algebra. If $q^2\neq 1$, then ${{k}_{{{q}^{-2}}}}[x,{{x}^{-1}},y]$ is isomorphic to $U_q({\mathfrak sl}_2)^{\>0}$, the non-negative part of the quantum enveloping algebra $U_q({\mathfrak sl}_2)$ as a Hopf algebras. Under the assumption that $q$ is not a root of unity, we investigate the coalgebra automorphism group of $k_q[x, x^{-1}, y]$. We describe the structures of the graded coalgebra automorphism group and the coalgebra automorphism group of $k_q[x, x^{-1}, y]$, respectively.
Relative regularity and Drazin inverses
Jianlong Chen
Department of Mathematics, Southeast University
jlchen@seu.edu.cn
Abstract: In this talk, we will discuss relative regularity and Drazin inverses in rings. It contains two parts. The first part is about relative regularity. We will give some progress of morphic ring, quasimorphic ring, (uniquely) clean ring ,(uniquely) strongly clean ring. The second part is about Drazin inverses and polar property. We will introduce quasipolar ring and pseudopolar ring. These are relative to generalized Drazin inverse and pseudo Drazin inverse. The relationship between strongly clean ring and quasi(pseudo)polar ring is given, and quasi(pseudo) polar matrix and triangular matrix rings are characterized. Also, we obtain Jacobson lemma and Cline formula about generalized Drazin inverse. Finally, we present some open questions.
Leavitt path algebras and singularity categories
Xiaowu Chen
School of Mathematics, University of Science and Technology of China
xwchen@mail.ustc.edu.cn
Abstract: Recent research indicates that Leavitt path algebras are related to both the singularity categories of algebras with radical square zero and the compact completion of singularity categories. In this talk, we explain their relation and recent progress. In particular, Leavitt path algebras relate further to the stable categories of Gorenstein projective modules.
Quantum affine $\mathfrak{g}{{\mathfrak{l}}_{n}}$ and affine $q$-Schur algebras
Qiang Fu
Department of Mathematics, Tongji University
q.fu@hotmail.com
Abstract: We will review some results about quantum affine $\mathfrak{gl}_n$ and affine $q$-Schur algebras. In particular, we will talk about affine Schur--Weyl duality, BLM realization problem of quantum affine $\mathfrak{gl}_n$ and representations of affine $q$-Schur algebras.
On finite- and infinite-dimensional representations of quantum groups of type A
Naihong Hu
Department of Mathematic, East China NormalUniversity
nhhu@math.ecnu.edu.cn
Abstract: We will talk about finite and infinite dimensional representations of type Aboth at roots of unity and generic case. These contains some discussions on Leowy filtration of indecomposable modules at roots of unity and some construction for infinite dimensional generalized projective modules at generic case. These are joint work with Gu Haixia and Wang Shenyou.
The Construction of Proper Resolutions and Applications
Zhaoyong Huang
Department of Mathematics, Nanjing University
huangzy@nju.edu.cn
Abstract：It is shown how to construct a (strongly) proper resolution of one term in a short exact sequence from that of the other two terms, and then the construction is applied to the study of the properties of Gorenstein categories and modules satisfying the Auslander condition.
Representations of the vertex operator algebra $V_{{{L}_{2}}}^{{{A}_{4}}}$
Cuipo Jiang
Department of Mathematics, Shanghai Jiaotong University
cpjiang@sjtu.edu.cn
Abstract：The rationality and $C_2$-cofiniteness of the orbifold vertex operator algebra $V_{{{L}_{2}}}^{{{A}_{4}}}$ are established and all the irreducible modules are constructed and classified. This is a joint work with Chongying Dong.
On the first Hochschild cohomology of admissible algebras and path algebras with oriented cycles
Fang Li
Department of Mathematics, Zhejiang University
fangli@zju.edu.cn
Abstract：In this talk, we try to find a method to construct the bases of the first Hochschild cohomology for some path algebras with certain relations. For path algebras whose quivers have cycles, we introduce the so-called graded version of Hochschild cohomology so as to be characterized
Representation type of super cocommutative Hopf algebras
Gongxiang Liu
Department of Mathematics, Nanjing University
gxliu@nju.edu.cn
Abstract：The classification of super cocommutative Hopf algebras of finite representation type is given. We show that the restricted cohomology algebra of a basic classical Lie superalgebra is finitely generated. By this result, we prove that the restricted enveloping algebra of basic classical Lie superalgebra g is always wild except $g=sl_2$ or $g=osp(1|2)$ or $g=C(2)$.
Progress on the classification of Artin-Schelter Regular Algebras
Diming Lu
Department of Mathematics, Zhejiang University
dmlu@zju.edu.cn
Abstract: The talk is about the classification of Artin-Schelter regular algebras. We will review some basic methods and report recent studies on the topic.
Tubular triangulated categories
Claus Michael Ringel
University of Bielefeld, and Shanghai Jiaotong University
ringel@math.uni-bielefeld.de
Abstract: The usual setting for questions in representation theory are abelian categories (of modules or sheaves), but In recent years a lot of attention has been shifted to triangulated categories (as they arise as stable module categories for group algebras, or as the derived categories of an abelian category). Under suitable finiteness conditions such triangulated categories are Krull-Remak-Schmidt categories with Auslander-Reiten triangles, and one may look at the shape of the corresponding Auslander-Reiten components. Of special interest seem to be triangulated categories which are tubular (so that all AR-components are tubes), since they occur quite frequently on the border line between finite (or discrete) type and wild type. The lecture will focus the attention to a typical class of examples, namely the category of modules over the preprojective algebras of type A_n which are cogenerated by a fixed indecomposable injective module. According to Geiss-Leclerc-Schroeer, these categories play an important role when studying the cluster structure on the coordinate ring of some Grassmannians. Note that here we deal with what is called an ADE-chain. For n = 8 one obtains a tubular triangulated category and we will outline in which way a classification of all the indecomposables can be achieved.
(This is a report on joint investigations with B. Leclerc and M. Schmidmeier.)
Character and dimension formulas for queer Lie superalgebras
Yucai Su
Department of Mathematics, Tongji University
ycsu@tongji.edu.cn
Abstract: Using Brundan's algorithm, we obtain closed character and dimension formulas for queer Lie superalgebras. This is a recent joint work with R.B.Zhang.
Gorenstein homological theory for differential modules
Jiaqun Wei
Department of Mathematics, Nanjing Normmal University
weijiaqun@njnu.edu.cn
Abstract：It is shown that a differential module is Gorenstein projective (injective, resp.) if and only if its underlying module is Gorenstein projective (injective, resp.). Extending Ringel-Zhang Theorem, we prove that, for a ring R, there is a bijective correspondence between projectively stable objects of split perfect differential modules and R-modules of projective dimension not more than 1, given by the homology functor H and stable syzygy functor. The correspondence sends indecomposable objects to indecomposable objects.
Calabi-Yau algebras and their homologies
Quanshui Wu
School of Mathematics, Fudan University
qswu@fudan.edu.cn
Abstract: In this talk, I will first remind the audience of the definition of the hochschild (co)homology, cyclic (co)homology and poisson (co)homology, then I will skech a way how to use the poisson (co)homology of poisson algebras to calculate the hochschild (co)homology and cyclic (co)homology for the lower dimensional graded Calabi-Yau algebras.
Decomposition matrices of cyclotomic NW and BMW algebras
Xu Xu
Department of Mathematic, East China Normal University
b03151241@yahoo.com.cn
Abstract. Motivated by Martin and Cox-De Visscher's work on the decomposition matrices for Brauer algebras and walled Brauer algebras over the complex field together with Rui and Si’s work on the blocks of cyclotomic Nazarov-Wenzl algebras and cyclotomic BMW algebras, we give an algorithm to compute the decomposition matrices on the cyclotomic Nazarov-Wenzl algebras and cyclotomic Birman- urakami-Wenzl algebras over the complex field with some additional assumptions. Our result shows that the multiplicity-free theorem holds for such algebras.
Filtered module categories and related homological conjectures
Yu Ye
School of Mathematics, University of Science and Technology of China
yeyu@ustc.edu.cn
Abstract: Let $A$ be a finite dimensional algebra and $Filt(A)$ the filtered module category of $A$. In this talk, I will consider the Grothendieck group of the category $Filt(A)$ and show that several homological conjectures, including the Cartan Determinant Conjecture, hold true for this category . Moreover, we will also discuss how these conjectures for $Filt(A)$ relate to the ones for $A$.
Gorenstein-projective modules and symmetric recollements
Pu Zhang
Department of Mathematics, Shanghai Jiaotong University
pzhang@sjtu.edu.cn
Abstract： We introduce compatible bimodules. The Gorenstein-projective modules over algebra $\Lambda =\left( \begin{matrix} A & M \\ 0 & B \\ \end{matrix} \right)$ are explicitly described, under the condition that $M$ is a compatible $A$-$B$-bimodule. This generalizes and unifies the corresponding results in [LiZ], [IKM], [XZ] and [LuZ]. If $\Lambda$ is Gorenstein, this description implies that $M$ is compatible. This description of ${\mathcal{GP}(\Lambda)}$ also suggests a recollement. As an application, it is proved that if $M$ is compatible, then there is a left recollement of the stable category ${\mathcal{GP}(\Lambda)}$; and that if $\Lambda$ is Gorenstein and $_AM$ is projective, then there is a symmetric recollement of the singularity category $D_{\text{sg}}^{b}(\Lambda )$ (here symmetric recollement is in the sense of P. Jrgensen [J]). For this, inspired V. Franjou and T. Pirashvili [FV], we give equivalent definitions of a recollement, applied to both triangulated categories and abelian categories.
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| 2012年06月29日（开会日期：June 9-June 29, 2012）
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Sponsors:East China Normal University
National Natural Science Foundation of China
Date:June 9-29, 2012
ECNU Summer School and workshop on Lie theory and representation theory III, June 9-29, 2012" will be held at the new campus of East China Normal University in Min Hang District of Shanghai.
This summer school and workshop is sequent to the former two held in 2006 and 2009 respectively
(to see http:/math.ecnu.edu.cn/academia/li2009 for the former).
This time we invite 5 mathematicians to give 5 mini-courses, focusing on representation theory with connection to geometry, in the 3-weeks summer school.
On the 17th and the 18th , and in the morning of 19th of June, there will be a workshop.
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| 2011年11月13日（开会日期：2011年11月12~13日）
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《曹锡华数学论坛6周年暨校庆60周年学术会议》
2010年11月12~13日 华师大闵行校区教师之家 多功能厅321
Nov. 12:
8:30—9:00 Openning (主旨发言: 王建磐)
Chair: 谈胜利
9:00—9:30 时俭益
9:30—10:00 张继平
10:00—10:30 Tea break & Photo
Chair: 王建磐
10:30—11:00 王跃飞
11:00—11:30 惠昌常
11:30—12:00 秦厚荣
12:00—13:30 Lunch
Chair: 张继平
14:00—14:30 张瑞斌
14:30—15:00 C. Ringel
15:00—15:30 胡 峻
15:30—15:45 Tea break
Chair: 芮和兵
15:45—16:15 吴泉水
16:15—16:45 刘治国
16:45—17:15 苏育才
Nov. 13
Chair: 胡乃红
8:30—9:00 朱 彬
9:00—9:30 李 方
9:30—10:00 朱胜林
10:00—10:30 Tea break
Chair: 舒 斌
10:30—11:00 杜 荣
11:00—11:30 姜翠波
11:30—12:00丁南庆
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学术报告摘要 (2011.11.12~13)
Relative coherence of rings
丁南庆，南京大学
Abstract: Recall that R is a left coherent ring if every finitely generated left ideal of R is finitely presented. This kind of rings was introduced by Chase (Chase S. U., Direct products of modules. Trans. Amer. Math. Soc. 1960, {97}: 457-473) as a generalization of left Noetherian rings. His characterization of coherence has led to a number of similar characterizations of coherence with respect to particular torsion pairs.
Let $\tau$ be a hereditary torsion pair for the category of left R-modules. Jones called R a $\tau$-coherent ring in case every finitely generated left ideal is $\tau$-finitely presented (Jones, M.F., Coherence relative to a hereditary torsion theory. Comm. Algebra 1982, {\bf 10}: 719-739).
In this talk, we introduce relative coherence of rings from another point of view. A ring R is called left $\tau$-coherent in case every $\tau$-finitely presented left ideal is finitely presented. To characterize $\tau$-coherent rings, $\tau$-flat and $\tau$-f-injective modules are introduced. A right R-module M is called $\tau$-flat if Tor_{1}(M,R/I)=0 for any $\tau$-finitely presented left ideal I. A left R-module N is said to be $\tau$-f-injective in case Ext^{1}(R/I, N)=0 for any $\tau$-finitely presented left ideal I. It is shown that there are many similarities between coherent rings and $\tau$-coherent rings. For instance, we prove that a ring R is left $\tau$-coherent if and only if any direct product of R_{R} is $\tau$-flat if and only if any direct product of $\tau$-flat right R-modules is $\tau$-flat if and only if any direct limit of $\tau$-f-injective left R-modules is $\tau$-f-injective if and only if every right R-module has a $\tau$-flat preenvelope. Some known results are extended.
This talk is a report on joint work with Lixin Mao.
Strict positivity of new numerical invariants and their applications
杜荣, 华东师大
Abstract: We introduce some new invariants for surface singularities and show that these invariants are strictly positive for rational surface singularities and quasi-homogeneous surface singularities. As an application, we relate one of these invariants with a CR invariant to solve complex Plateau problem.
Quiver Schur algebras
胡峻，北京理工大学
Abstract: I will talk about some recent progress on the construction of a graded quasi-hereditary covering for the cyclotomic quiver Hecke algebras associated to the linear quivers. These algebras are quasi-hereditary graded cellular algebras. My talk is based on a joint work with Andrew Mathas.
A characterization of vertex operator algebras V ^ +_Z\alpha
姜翠波
Abstract: We give the characterization of vertex operator algebra V^ +_Z\alpha. This result contributes to the classification of rational vertex operator algebras of central charge 1.
Topological quivers and mutation types
李方，浙江大学
Abstract： 我们希望考虑箭图的拓扑结构对于由箭图决定的代数结构有什么样的影响。我们分三个方面来阐明这个问题：有限维遗传代数的一阶Hochschild上同调的李代数基与箭图亏格的关系；遗传代数上倾斜(tilting)模的倾斜箭图的亏格；丛(cluster)代数的亏格对于变异(mutation)型的影响。
Some mathematical discoveries of Ramanujan and recent progress
刘治国，华东师大
Abstract： Srinivasa Ramanujan (22 December 1887--26 April 1920) was a renowned mathematician in the history of modern mathematics. In spite of having no formal ematics, Ramanujan made substantial contributions in the areas of mathe matical analysis, number theory, combinatorial analysis, infinite series and con. In this talk we will introduce some remarkable mathematical discoveries of Ramanujan and recent progress.
An Expression For Primes And Its Application To $K_2\Bbb Q$
秦厚荣，南京大学
Abstract: We show that any prime $p\equiv 1\pmod 8$ is a quotient of the finite products of the form $a^4+b^4$. Applying this result we obtain a generating set for the subgroup of $K_{2}\mathbb Q$ consisting of all elements of order dividing 8.
Representations of a quiver over the ring of dual numbers
C. Ringel, Bielefeld University & Shanghai Jiaotong University
Abstract: Let Q be a finite connected directed quiver and k a field. The representations of the path algebra kQ have been studied for a long time, and one knows quite well the structure of the module category mod kQ; it is an abelian category with enough projectives and injectives. Unfortunately, the existence of the projective and the injective representations leads to some symmetry break, since the Auslander-Reiten shift is not defined for the indecomposable injective representations. For example if Q is representation-infinite, we obtain two Auslander-Reiten components which ought to be connected in some way, as it is done in the cluster category of type Q (but there one has to introduce new objects).
We are going to exhibit a triangulated category which provides the required additional maps without introducing new objects, namely the homotopy category of the category D of perfect differential kQ-modules. Note that differential kQ-modules are just the representations of the quiver Q over the k-algebra k[epsilon] of dual numbers. We will show that the perfect differential kQ-modules are just the torsionless kQ[epsilon]-modules, and therefore the Gorenstein-projective kQ[epsilon]-modules. The homology functor H from D to mod kQ furnishes a bijection between the indecomposable non-projective Gorenstein-projective kQ[epsilon]-modules and the indecomposable kQ-modules, as well as an embedding of the Auslander-Reiten quiver of mod kQ into the Auslander-Reiten quiver of the homotopy category of D.
This is a report on current joint investigations with Zhang Pu (SJTU).
Cells of the affine Weyl group $\widetilde{C}_n$ in a quasi-split case
时俭益，华东师大
Abstract: After a brief review on the study of Kazhdan-Lusztig cells of the Coxeter groups with equal and unequal parameters, I report my recent work on the affine Weyl group $\widetilde{C}_n$in a quasi-split case.
Quasifinite Representations of Block Type Lie Algebras
苏育才， 同济大学
Abstract: Let $B$ be the Block type Lie algebra over $\mathbb{C}$ with basis $\{L_{\alpha,i},C_1,C_2|(\alpha,i)\in\mathbb{Z}\times\mathbb{Z}\backslash\{(0,-2)\}\}$ and Lie bracket $[L_{\alpha,i},L_{\beta,j}]=(\beta(i+1)-\alpha(j+1))L_{\alpha+\beta,i+j}+\alpha\delta_{\alpha+\beta,0}\delta_{i+j,-2}C_1+(i+1)\delta_{\alpha+\beta,0}\delta_{i+j,-2}C_2$,where $C_1,C_2$ are central elements. In this talk, it is proved that a quasi-finite irreducible $B$-module is either a highest or a lowest weight module. We also give a classification of all highest/lowest weight $B$-modules. This is a joint work with Ming Gao and Yun Gao.
Dynamics on Berkovich Space
王跃飞，中国科学院数学与系统科学研究院
Abstract. We will talk about the dynamical systems on the Berkovich projective space and its applications on commuting p-adic dynamical systems.
Calabi-Yau and twisted Calabi-Yau algebras
吴泉水，复旦大学
Comparison of representations of algebras and their swich algebras
惠昌常，北京师大
Abstract: One of the central problems in representation theory is to understand the irreducible representations. A strategy used very often for attacking this problem is to link the representation theory of a given algebra to the one of another algebra for which the representation theory is understood in a certain sense. In this talk, we shall provide a general method by comparison of the representation theories of algebras and their swich algebras. As a result, one has a classification of all irreducible representations of affine cellular algebras.
This is a part of a joint work with Steffen Koenig.
The rank of a fusion system
张继平，北京大学
Abstract: In the early 1990's, Puig created his theory of fusion systems as a tool in modular representation theory. Later, Broto, Levi and Oliver used this theory to provide a formal setting for, and prove results about the $p$-completed classifying spaces of finite groups. Aschbacher started a program to establish a local theory of fusion system similar to the local theory of finite groups. We introduce here the notion of the rank of asaturated fusion system and prove some basic results about weakly normal subsystemsand factor systems.
Finitely generated projective modules over quantum symmetric algebras
R. B. Zhang, Sydney University & 中科大
Abstract: Many quantised coordinate algebras arising from the context of quantum groups are non-commutative analogues of symmetric algebras over finite dimensional vector spaces. We discuss the finitely generated projective modules and higher algebraic K-groups of such quantum symmetric algebras.
Cluster strucures in a 2-CY triangulated category
朱彬，清华大学
Abstract: 2-CY triangulated categories are often to be used to categorify cluster algebra via cluster tilting objects. Maxiaml rigid objects are a generalization of cluster tilting objects.There are2-CY categories without cluster tilting objects, but maximal rigid objects (cluster tubes are such an example). In this talk, I will talk about how to use cluster tubes to categorify cluster algebras of type C via maximal rigid objects.
Smash products of H-simple module algebras
朱胜林，复旦大学
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学术会议
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