Visitors List
2024
August 20-22 Prof. Dr. Javad Asadollahi (Univ.
Isfahan)
August 10-11, 13-14 Dr. Merlin Christ (Inst. Math. Jussieu)
July 12-15 Dr. Qiang Dong (SJTU)
March 29 Prof. Dr. Roozbeh Hazrat
(Western Sydney Univ.)
Title: Bergman algebrasTime: 16:30-17:30, Location 1318
Abstract: A half a century ago, George Bergman introduced stunning machinery which would realise any commutative conical monoid as a K-theory of a ring. We discuss this machinery. Many combinatorial algebras constructed in the last 50 years, such as Leavitt path algebras and their generalisations, can be obtained from Bergman’s machinery. 2023
Dec. 7-Jan. 5, Miantao Liu (Univ. Paris Cite)
Nov. 27-30 Dr. Jiahao Cheng (Nanchang Hangkong Univ.)
Title: Deligne’s conjecture for Lie algebroid pairsTime: Nov. 29, 15:00-16:00, Location 5405
Abstract: Deligne conjectured that the Hochschild cochain complex of an associative algebra admits a structure of an algebra over the little 2-discs operad. Braces algebras play important roles in the solutions of Deligne’s conjecture. The theory of Lie algebroid pairs provides a common framework to study many sources of geometric objects which include complex manifolds, foliations, and manifolds with Lie algebra actions. In this talk, I report progress on constructing homotopy braces algebra arising from a Lie algebroid pair, and proving a geometric generalization of Deligne’s conjecture: the Hochschild cochain complex of a Lie algebroid pair also admits a structure of an algebra over the little 2-discs operad. This is a joint work with Z. Chen, Y. Qiao, and M. Xiang.
Nov. 21-Dec. 5, Junyang Liu (Tsinghua Univ.)
Nov. 19-Jan. 5, Prof. Dr. Bernhard Keller
(Univ. Paris Cite)
Title: On the structure of Calabi-Yau algebras and categoriesTime: Nov. 24, 10:00-11:30, Location 1318Time: Nov. 30, 14:30-16:00, Location 1318Time: Dec. 7, 14:00-15:30, Location 1318Time: Dec. 15, 10:00-11:30, Location 1318Time: Dec. 21, 14:15-15:45, Location 1318Time: Dec. 28, 14:30-16:00, Location 1318 Abstract: In this lecture series, we will present structure theorems for Calabi-Yaualgebras and categories following mainly work by Michel Van den Bergh and recentjoint work with Junyang Liu. Calabi-Yau algebras can be viewed as non-commutativeanalogues of symplectic varieties and the structure theorems we will present will benon-commutative analogues of Darboux' theorem, which states that locally, eachsymplectic variety is isomorphic to affine 2n-space with its standard symplectic structure. Of course, the locality condition is essential here. In the non-commutativecontext, it is replaced with the assumption that our algebras are (connective, complete augmented) pseudo-compact dg (=differential graded) algebras (andsimilarly for categories and for functors). The lecture series will consistof two main parts, the first one being devoted to the structure of Calabi-Yaudg algebras and morphisms and the second one to that of Calabi-Yau triangulated categories and stably Calabi-Yau Frobenius categories. In the first part, after an introduction with examples, we will first recall the necessary homological algebra and the Calabi-Yau conditions for algebras in the absolute and the relative (pseudo-compact) setting. We will then present the Darboux theorems in the absolute case (due to MichelVan den Bergh) and the relative case (obtained in joint work with Junyang Liu).In the second part, we will start with a reminder on cluster categoriesconstructed from quivers with potential (following Amiot and Lingyan Guo) and Higgs categories constructed from ice quivers with potential (following Yilin Wu). We will then sketch how, via a "dimension shift", the results of the first part allow to prove that algebraic d-Calabi-Yau categories with cluster-tilting object are cluster categories associated with (d+1)-Calabi-Yau algebras (absolutecase) and that certain stably d-Calabi-Yau Frobenius exact categories areHiggs categories (relative case). These statements can be viewed as proofs of variants of Amiot's conjecture from 2010.
August 22-27, Prof. Dr. Yinhuo Zhang (Univ. Hasselt)
Title: Representation rings of the small (quasi-)quantum groupsTime: 7.23，16:30-17:30, Location: 1418
Abstract: In this talk, we introduce a class of finite dimensional quasi-Hopf algebras, called small quasi-quantum groups, and compute their representation rings. It turns out that their stable representation rings are isomorphic to the ones of the classic small quantum groups.
August 21-25, Dr. Zhengfang Wang
(Univ. Stuttgart)
July 17-19, Dr. Weinan Zhang (Univ. Virginia)
Title: Drinfeld type presentations for affine i-quantum groupsTime: 7.18，10:00-11:00, Location: 1418
Abstract: The Drinfeld (loop) presentation for affine quantum groups has played a fundamental role in its representation theory. The i-quantum groups are coideal subalgebras of quantum groups arising from quantum symmetric pairs, and they can be viewed as natural generalizations of quantum groups. In this talk, I will talk about our recent construction of Drinfeld type presentations for quasi-split affine i-quantum groups. This new Drinfeld type presentation can be thought as a deformation of the Drinfeld presentation for affine quantum groups. This is joint with Ming Lu and Weiqiang Wang.
July 5-8, Prof. Dr. Naihuan Jing (North Carolina State Univ.)
Title: McKay-Slodowy correspondence and tensor invariants
Time:
July 6, 10:00-11:00
Location:
1418
Abstract: We will first review the McKay correspondence and its generalization
using elementary group theory. It gives a nice correspondence between finite
subgroups of SL(2, C) and simply laced affine Dynkin diagrams. The McKay-Slodowy
correspondence is then used to describe tenor invariants and symmetric tensor invariants.
We also discuss generalization to higher rank case.
Title: Quantum affine algebras and extended quantum affine algebras
Time: July 7, 10:00-11:00
Location:
1418
Abstract: Quantum affine algebras are quantum enveloping algebras of affine Lie algebras,
introduced independently by Drinfeld and Jimbo in their study of the Yang-Baxter equation.
Representation theory of quantum affine algebras depends mostly on the Drinfeld realization.
We will discuss our recent joint work with F. Chen, F. Kong and S. Tan on Drinfeld realization
for quantum extended affine algebras.
June 15-21, Prof. Dr. Zongzhu Lin (Kansas State Univ.)
Title: Unifying highest weight modular representation theories
Time:
16, 17, 19, 20, 22,
10:00-11:30
Location:
1418
Abstract: Given a generalized Cartan matrix, there are many different algebras and groups
one can attach to, the classical Kac-Moody Lie algebra and the corresponding Kac-Moody
groups as well as quantum groups (superquantum groups) with one or many parameters
appearing in the literature. One of the themes in representation theories of these algebras is to
compute the decomposition numbers of irreducible modules in the universal highest weight
modules. More generally, one want to study the Kazhdan-Lusztig theory, in particular,
one wants to compute the Kazhdan-Lusztig polynomials. In this series of lectures, we will
define Lusztig's modified quantum groups, called U-dot system, for each of these algebras.
It turns out that the highest weight representations of these algebras are dependent only
on the U-dot systems. We will prove that the U-dot systems are isomorphic up to base change.
Thus one can compare different highest weight representation theories of different types
of quantum groups/algebras by comparing their U-dot systems. Therefore their decomposition
numbers as well as the Kazhdan-Lusztig polynomials can be transported freely among different
quantum groups or algebraic groups as well as their modular representation theories. Lusztig's
various conjectures in the path of proving Lusztig's character formula conjecture for algebraic
groups in positive characteristic case using representations of quantum groups, representations
of affine Kac-Moody Lie algebras is, in fact, to compare the U-dot systems. This is a joint
work with Zhaobin Fan and Yiqiang Li.
May 12, Prof. Dr. Caiheng Li
(Southern Univ. of Science and Technology)
Title: Factorizations of finite groups
Time:
14:30-15:30
Location:
5505
Abstract: Studying factorizations of groups is a lastingly active topic in group theory, and
has many applications in various areas. The factorization problem of almost simple groups
has been one of the central problems in finite simple group theory. The problem has been
reduced to determine factorizations of classical groups of Lie type. In this talk, I will report
on recent progress of the problem.
May 5, Dr. Jinbi Zhang (Peking Univ.)
Title:
The left-right symmetry of
finite delooping level
Time:
10:00-11:00
Location:
5106
Abstract: In this talk, we will show that the delooping level conjecture holds true for
all Artin algebras if and only if, for all Artin algebras, the delooping level of an algebra
being finite implies that the delooping level of its opposite algebra is also finite. This is
based on a joint work with YongLiang Sun.
Mar. 3, Prof. Dr. Changchang Xi (Capital Normal Univ.)
Title: Stable equivalences of centralizer matrix algebras
Time:
16:30-17:30
Location:
1418
Abstract: In the representation theory of algebras and groups, stable equivalences
have been investigated for a long time. They are, however, still remain mysterious.
One of the main conjectures on stable equivalences is the Auslander-Reiten (or
Auslander-Alperin) conjecture which states that two stably equivalent algebras
should have the same number of non-isomorphic, non-projective simple modules.
This conjecture is open up to date. In this talk, we will show that the Auslander-Reiten
conjecture on stable equivalences holds true for a class of centralizer matrix algebras
over algebraically closed field and reveal 3 new invariants of stable equivalences
of Artin algebras. This talk presents a joint work with J.B. Zhang.
Feb. 11, Prof. Dr. Zhaobing Fan (Harbin Engineering Univ.)
Title:
The positivity of the
canonical basis under the comultiplication
Time:
16:00-17:00
Location:
1418
Abstract: We show the positivity of the canonical basis for a modified quantum affine
sln and modified i-quantum groups under the comultiplication. This is a joint work
with Yiqiang Li.
2022
Dec. 16, 23, 30, Prof. Dr. Bernhard Keller
(Univ. Paris Cite)
Title: An introduction to exact dg categories,
after Xiaofa Chen
Time: 10:00-11:30
Location:
1408
Abstract: In this series of lectures, we will report on results from Xiaofa Chen's
ongoing Ph. D. thesis. His notion of an exact dg category is a simultaneous
generalization of the notions of exact category in the sense of Quillen and
of pretriangulated dg category in the sense of Bondal-Kapranov. It is also a dg
enhancement of the notion of extriangulated category recently introduced by
Nakaoka-Palu. Via Lurie's dg nerve, it is related to Barwick's notion of exact
infinity-category.
We will start by recalling the definition and the main examples of extriangulated
categories. We will then give the definition of an exact dg category in complete
analogy with Quillen's but where the category of kernel-cokernel pairs is replaced
with a more sophisticated homotopy category. We will give two descriptions of this
category using respectively dg functor categories and A-infinity functor categories.
We will then present examples related to Yilin Wu's Higgs categories and Haibo Jin's
categories of dg Cohen-Macaulay modules. There will follow a number of fundamental
results concerning the dg nerve, the dg derived category, tensor products and functor
categories with exact dg target and the existence of the greatest exact structure on a dg
category with additive H^0. This generalizes a Theorem of Rump for Quillen exact
categories. Under certain hypotheses, it allows to classify all exact structures on a given
dg category with additive zeroth homology. Finally, we will present work in progress
with Yilin Wu and Xiaofa Chen on the subtle notion of projective respectively injective
resolution for objects in exact dg categories.
A Series of Online Talks
supported by NNSF and Wu Wen-Tsun Key Lab.
Math.
May 27, Prof. Dr. Nanqing Ding
(Nanjing Univ.)
Title: On Pure Acyclic Complexes
Time: 14:30-15:30
Location:
5205, Tencent 518-5448-0979
Abstract: In this talk, we review some results on pure acyclic complexes and give an
affirmative answer to the conjecture that a complex $E$ in a locally $\lambda$-presentable
Grothendieck category $\mathcal{A}$ is $\lambda$-pure acyclic if and only if any chain
map $ f : X\rightarrow E$ from a complex $X$ of $\lambda$-pure projective objects
in $\mathcal{A}$ to $E$ is null-homotopic, where $\lambda$ is an infinite regular cardinal.
This talk is a report on joint work with Lei Shen and Meiqi Wang.
May 13, Prof. Dr. Fang Li (Zhejiang
Univ.)
Title: 丛代数的散射图理论与分母向量正性问题
Time: 14:30-15:30
Location:
5205, Tencent 518-5448-0979
Abstract: 在这个报告，我们首先介绍丛代数的散射图理论，然后用它解决可斜
对称化丛代数的分母向量正性猜想。同时介绍下这个猜想的最近进展。本研究
与曹培根和潘杰合作。
May 6, Prof. Dr. Jun Hu (Beijing
Institute of Tech.)
Title: On the center conjecture for the
cyclotomic KLR algebras
Time: 14:30-15:30
Location:
5205, Tencent 518-5448-0979
Abstract: The cyclotomic KLR algebras play an important roles in the categorification
of integrable highest weight modules of quantum groups. The center conjecture for the
cyclotomic KLR algebras $R_\beta^\Lambda$ asserts that the center of $R_\beta^\Lambda$
consists of symmetric elements in its KLR $x$ and $e(\nu)$ generators. In this talk, I will
report some history and our recent progress on this conjecture. This talk is based on a joint
work with Lin Huang.
April 22, Prof. Dr. Jie Xiao (Tsinghua
Univ.)
Title: 二周期范畴的李代数
Time: 14:30-15:30
Location:
5205, Tencent 518-5448-0979
Abstract: 由二周期三角范畴上内蕴构造李代数（彭联刚-肖）。可以在二周期的
导出范畴上建立一个拓扑，使支撑集为不可分解对像的可构函数按卷积乘积的
方括号运算实现这一李代数（肖-徐帆-张光连），当考虑遗传代数（quiver表示）
的根范畴时，这一构造实现了Kac-Moody李代数。另一方面，对二周期投射复
形范畴Bridgeland 构造了Hall 代数，在遗传代数的二周期投射复形范畴时，
Bridgeland 的Hall代数同构于Ringel-Hall 代数的Drinfeld double 。我们希望
调查这两种构造的联系。最近，方杰鹏、兰以心的合作给出了这个问题的答案。
为此，我们首先构造Bridgeland的Hall代数的motivic 形式。这个motivic 版本
在其Poincare 多项式中取t等于-1有一个退化（极限）李代数，由支撑集为不可
分解的radical 复形的可构函数生成。我们的主要定理是由二周期投射复形范畴
到其稳定三角范畴的自然函子诱导了这两个李代数的典范同构；这意味着，
Bridgeland 的Hall 代数产生的李代数其结构常数是对应三角范畴的三角所内蕴
计数的。
April 8, Prof. Dr. Zhongkui Liu
(Northwest Normal Univ.)
Title: Relative cohomology groups and Gpp
dimensions of complexes
Time: 14:30-15:30
Location:
5205, Tencent 518-5448-0979
Abstract: We establish a relationship between the vanishing of relative cohomology
groups and the finiteness of Gpp dimensions of complexes. This is a Gorenstein
version of a conclusion established by Avramov and Foxby. Hence it is valuable
to study further Gpp dimensions of complexes.
April 1, Prof. Dr. Changchang Xi (Capital Normal Univ.)
Title: Orthogonal generators over self-injective
algebras
Time: 14:30-15:30
Location:
5205, Tencent 518-5448-0979
Abstract: One of the main open problems in the representation theory of Artin
algebras is the Nakayama conjecture, stating that an Artin algebra should be
self-injective whenever its dominant dimension is infinite. To attack
this conjecture, Tachikawa proposed two related conjectures, one of them
says that an orthogonal module over a self-injective algebra should be
projective. Motivated by these conjectures, we study orthogonal generators over
self-injective algebras from the angle of triangulated categories. In the talk we will
show that such modules produce recollements of relative stable module categories
and discuss their dimensions. As a consequence, we show that the Nakayama
conjecture holds true for the universally Gorenstein algebras. This reports parts
of a recently ongoing work jointly with H. X. Chen.
2021
For visitor list and talks, we refer to the
page maintained by Ren Wang.
2020
12.27-29 Dr. Peigen Cao
12.26 Prof. Dr. Yu Qiu (Tsinghua
Univ.)
Title: Topological realization of
Lagrangian immersions
Time: 12.26, 16:00-17:00
Location:
GuanLiKeYan Building, Room 1318
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.
12.24-1.9 Yu Wang (Nanjing Univ.)
12.21-1.13 Junyang Liu (Tsinghua Univ.)
2019
11.29-12.1 Prof. Dr. Nan Gao (Shanghai Univ.)
Title: A functorial approach to
monomorphism categories for species
Time: 11.30, 16:00-17:00
Location:
GuanLiKeYan Building, Room 1418
Abstract: We investigate abstract versions of the monomorphism category as studied by Ringel and
Schmidmeier. We prove that analogues of the kernel and cokernel functor send almost split sequences
over the path algebra and the preprojective algebra to split or almost split sequences in the
monomorphism category. This is based on the joint work with Julian Kuelshammer,
Chrysostomos Psaroudakis and Sondre Kvamme.
11.15-16 Prof. Dr. Xiaojin Zhang
(Nanjing Univ. Info. Sci. Tech.)
Title: From $\tau$-tilting modules to tilting
modules
Time: 11.15, 16:00-17:00
Location:
GuanLiKeYan Building, Room 1418
Abstract: In this talk, we recall some basic properties of $\tau$-tilting modules, especially
the homological properties of self-orthogonal $\tau$-tilting modules. Moreover, we give a
sufficient and necessary condition for a self-orthogonal $\tau$-tilting module to be a classical
tilting module. We show that a $\tau$-tilting module of finite projective dimension
is a classical tilting module if and only if it is self-orthogonal.
11.9-10 Dr. Dawei Shen (Henan Univ.)
08.19-25 Dr. Huanhuan Li (West.
Sydney Univ.)
07.26-27 Dr. Dawei Shen (Henan Univ.)
07.7-10 Dr. Zhengfang Wang
(Bonn)
07.4-7 Prof. Dr.
Xueqing Chen (Univ. Wisconsin-Whitewater)
Title: Introduction to quiver varieties
Time: 7.5, 9:00-11:00
Location:
05.11-13 Dr. Huanhuan Li (West.
Sydney Univ.)
04.23-29 Yilin Wu (ECNU)
04.21-28 Prof. Dr. Bernhard Keller
(Paris 7)
Title: From morphic enhancements to derivators
Time & Location: 4.23, 14:00-15:00, the fifth teaching
building 5506
4.24, 4.26, 4.27,
9:00-10:00, the math building 1218.
Abstract: It is well-known that in the derived category of an abelian category,
the cone is not functorial. However, it becomes functorial when we replace it
with the cone functor defined on the derived category of the category of
morphisms of the abelian category. Morphic enhancements axiomatize the relations
between the derived category and the derived category of morphisms. They allow
to define a triangulated structure on Krause's Cauchy completion of a (phantomless,
algebraic) triangulated category and to define a "realization functor" on two-term
complexes. By iterating morphic enhancements, one naturally arrives at the notion of
an epivalent tower of triangulated categories, which goes back to the late eighties.
It serves to formulate a universal property of the construction that assigns the
derived category to an exact category. In practice, all towers that occur are in fact
restrictions of derivators of the cubical category and it is natural to replace the tower
with the derivator. As shown by Porta, the stable derivator associated with an exact
category still enjoys a pleasant universal property.
04.21-27 Prof. Dr. Zheng Hua (Hongkong Univ.)
Title: On quivers with analytic potentials
Time & Location: 04.22, 15:00-16:00, the fifth teaching building
5305
Abstract: Given a finite quiver, an element of the complete path algebra over field of
complex number is called analytic if its coefficients are bounded by a geometric series.
We may develop a parallel construction of Jacobi algebra and Ginzburg algebra for
a quiver with an analytic potential. Analytic potential occurs naturally in the deformation
theory of sheaves on projective Calabi-Yau manifold. It turns out that analytic potentials
admit much richer structures in noncommutative differential calculus compared with the
formal ones. I will give a brief introduction to some of my recent work on this topic.
2018
11.5
Prof. Dr. Yanhua Wang (Shanghai)
Title: Discriminants of noncommutative algebras
and their applications
Time: 10:50-11:50
Location:
Abstract: In this talk, I will introduce the development of discriminants
of noncommutative algebras in recent years. Discriminant formulas of
some noncommutative algebras will be given. Applications of discriminants
in automorphism groups, isomorphism problems and Zariski cancellation
problems will be presented.
11.5
Prof. Dr. Yinhuo Zhang
(Hasselt)
Title: Finite quasi-quantum groups over finite
abelian groups
Time: 9:40-10:40
Location:
Abstract: In this talk, we study nondiagonal finite quasi-quantum groups over finite
abelian groups. We investigate the Nichols algebras in the twisted Yetter-Drinfeld
module category with a nonabelian 3-cocycle on a finite abelian group G. A complete
classification is obtained for the Nichols algebra B(V) in caseV is a simple twisted
Yetter-Drinfeld module of nondiagonal type. This provides a complete classification of
finite-dimensional coradically graded pointed coquasi-Hopf algebras over abelian
groups of odd order, and confirms partially the generation conjecture of pointed finite
tensor categories due to Etingof, Gelaki, Nikshych and Ostrik.
10.19
Dr. Zhibin Zhao (Anhui
Univ.)
Title: Some homological invariant properties
under Frobenius extensions
Time: 10:00-11:00
Location:
Abstract: Frobenius extensions were introduced by Kasch as a generalization of Frobenius
algebra. In this talk, we will show that, for a Frobenius extension, a module over the
extension ring is Gorenstein projective if and only if so is its underlying module over the
base ring. For a separable Frobenius extension between Artin algebras, we obtain that
some homological properties are invariant, including CM-finiteness, CM-freeness and the
representation dimension of Artin algebra.
08.25-27 Dr. Huanhuan Li (West.
Sydney Univ.)
07.25-26 Prof. Dr. Zheng Hua (Hongkong Univ.)
Title: Cluster category and birational geometry
Time: 07.25, 16:00
Location:
Abstract: A fundamental problem in birational geometry, in particular in minimal model
program, is to classify contractible rational curves. In this talk, we will build a relation
between it and the theory of cluster category. To be more specific, we associate to each
3-dimensional flopping contraction a cluster category in the sense of Aimot. Based on
our previous work on noncommutative Mather-Yau theorem, we show that the cluster
category is essentially determined by its cluster tilting algebra. On the other hand, we
formulate certain necessary condition on the associated cluster category for a rigid
rational curve to be contractible, which is conjecturally to be also sufficient. The talk is
based on a joint work with Guisong Zhou 1803.06128, and the work in progress joint
with Bernhard Keller.
06.12-06.15 Prof. Dr. Wei Ren (Chongqing
Normal Univ.)
05.06-05.11 Prof. Dr. Yu Qiu (CUHK)
Title: Topological type Fukaya categories and Calabi-Yau/Cluster categories.
Time: 05.08, 14:30-15:30
Location:
Abstract: We introduce Calabi-Yau-X categories of quivers with superpotential from
surfaces and show that their cluster categories are topological Fukaya categories. We
also survey various topological type Fukaya categories, including Calabi-Yau-3
categories of quivers with potential and Calabi-Yau-2 cluster categories from
surfaces. (Joint with Akishi Ikeda and Yu Zhou)
Title: Cluster exchange groupoids and framed quadratic differentials
Time: 05.09, 14:30-15:30
Location:
Abstract: We introduce cluster exchange groupoids, whose points groups give the
generalized braid groups--the cluster braid groups. As application, we
construct spaces of framed quadratic differentials on decorated marked
surfaces, that realized spaces of stability conditions, and show that
these spaces are simply connected. (Joint with Alastair King)
03.14-03.18 Prof. Dr. Hideto Asashiba (Shizuoka Univ.)
Title: Derived equivalence classification of selfinjective
algebras and 2-categorical covering theory
Time: 03. 15, 15:30-17:00, 03.16/17,
10:00-11:30
Location:
Abstract: Throughout the lectures all algebras are assumed to be finite-dimensional algebras
over a fixed algebraically closed field k. First we review the derived equivalence classification
of representation-finite selfinjective algebras and multifold extensions of piecewise hereditary algebras
of tree type, and see how a covering theory was used to show derived equivalences. Because we
have to deal with coverings of non-basic categories, we introduce weak group actions on k-categories,
which leads us to a 2-categorical covering theory. We explain how to use this theory to show derived
equivalences of algebras having forms of orbit categories of k-categories. Finally, by considering the
converse construction of orbit categories, we introduce a 2-categorical Cohen-Montgomery duality
and discuss relationships between these constructions and derived equivalences.
03.13-03.17 Prof. Dr. Zengqiang Lin (Huaqiao Univ.)
Title: Abelian quotients of the categories of short exact sequences
Time: 03.14, 10:00-11:00, 03. 15, 14:30-15:30
Location:
Abstract: We investigate abelian quotients of the categories of short exact sequences. The natural
framework to consider the question is via identifying quotients of morphism categories as
module categories. In the first talk, I will provide techniques needed for such identifications. These
ideas not only can be used to recover the abelian quotients produced by cluster-tilting subcategories
of both exact categories and triangulated categories, but also can be used to reach our goal. In the
second talk, I will focus on the properties of the abelian quotients. I will describe the abelian structure,
simple objects, projective objects and injective objects, which provide a new viewpoint to
understand Hilton-Rees Theorem and Auslander-Reiten theory.
01.23-01.30 Pengjie Jiao (Henan
Agricultural Univ.)
01.22-01.29 Dr. Dawei Shen (Henan Univ.)
01.22-01.24 Dr. Yiping Chen (Wuhan Univ.)
Title: Support variety theory is invariant under
singular equivalences
of Morita type
Time: 1.23, 10:00-11:00
Location:
Abstract: Using a new equivalent definition of support varieties in the
sense of Snashall and Solberg, we will show that both the $({\bf Fg})$
condition and support varieties are preserved under singular equivalences
of Morita type. In particular, support variety theory is invariant under
stable equivalences of Morita type.
01.14-01.15 Tiwei Zhao (Nanjing Univ.)
Title: Support τ-tilting modules and recollements
Time: 01.15, 10:00-11:00
Location:
Abstract: Let (mod A, mod B, mod C) be a recollement of abelian categories for
artin algebras A, B and C. Under certain conditions, we present an explicit
construction of gluing of (support) τ-tilting modules in mod B with respect
to (support) τ-tilting modules in mod A and mod C respectively; conversely,
we study the construction of (support) τ-tilting modules in mod A and mod C
obtained from (support) τ-tilting modules in mod B.
01.12-01.13 Dr. Peiyu Zhang (Anhui Polytech.
Univ.)
Title: Silting pair and relative
AR-correspondence
Time: 01.12, 15:00-16:00
Location:
Abstract: As a generalization of tilting pair, which was introduced by Miyashita, the notion
of a silting pair is introduced. We extend a characterization of tilting modules given by
Bassoni to silting pairs, and prove that there is an one-to-one correspondence between
silting pairs and certain subcategories.
2017
12.29-31 Prof. Dr. Zhi-Wei Li (Jiangsu Normal Univ.)
11.21-26 Dr. Zhengfang Wang (Peking Univ.)
11.3-4 Prof. Dr. Fei Xu (Shantou Univ.)
Title: Local representations of categories
Time: 11.3, 15:00-16:00
Location:
9.24-30 Dr. Huanhuan Li (West.
Sydney Univ.)
Title: Graded Steinberg algebra
Time: 9.25, 27, 10:30-11:30
Location:
Abstract: We consider the graded Steinberg algebra of a graded ample Hausdorff groupoid.
We show that this category is isomorphic to the category of unital left modules over the
Steinberg algebra of the skew-product groupoid arising from the grading. To do this, we show
that the Steinberg algebra of the skew product is graded isomorphic to a natural generalisation
of the Cohen-Montgomery smash product of the Steinberg algebra of the underlying groupoid
with the grading group. Specialising to the setting of directed graphs, we produce a
representation of the monoid of graded finitely generated projective modules over a Leavitt path algebra.
6.17-20 Prof. Dr. Chao Zhang (Guizhou Univ.)
5.20-27 Prof. Dr. Xueqing Chen (Univ.
Wisconsin-Whitewater)
Title: Introduction to orbit categories
Time: 5.23-26, 14:30-16:00
Location:
Abstract: see here.
4.7 Prof. Dr. Zhi Chen (Hefei Tech.
Univ.)
Title:
Objects related to generalized braid groups
Time: 4.7, 10:00-11:00
Location:
1.3-5 Prof. Dr. Wei Ren (Northwest
Normal Univ.)
Title:
Homotopy equivalences and recollements induced by cotorsion triples
Time: 1.4, 14:00-15:00
Location:
Abstract: click here.
2016
12.25-27 Dr. Zhenxing Di (Northwest Normal
Univ.)
Title:
An Auslander-Buchweitz approximation approach
to the silting theory in triangulated categories
Time: 12.16, 10:30-11:30
Location:
Abstract: click here.
10.13-14 Prof. Dr. Jiaqun Wei (Nanjing
Normal Univ.)
Title:
Repetitive equivalences and good Wakamatsu-tilting modules
Time: 10.13, 15:00-17:00
Location:
Abstract: Let $R$ be a ring and $T$ be a good
Wakamatsu-tilting module with $S = End_RT$.
We prove that $T$ induces an equivalence
between stable categories of repetitive algebras of $R$
and $S$.
10.11 Prof. Dr. Dingguo Wang (Qufu
Normal Univ.)
Title: Primitive cohomology of Hopf algebras
Time: 10.11, 10:00-11:00
Location:
Abstract: Primitive cohomology and dimension of
Hopf algebra are defined. Among many of
its applications, two classifications are
presented.
8.10-17 Dr. Dawei Shen (ECNU)
7.24-30 Prof. Dr. Zhe Han (Henan Univ.)
Title: Discrete derived categories
Time: 07.25, 26, 28, 29, 10:00-11:30
Location:
Abstract: We survey some results about discrete
derived categories. Roughly speaking, discrete
derived categories have less complexity
than derived categories of tame hereditary algebras. We
mainly focus on the components of their
Auslander-Reiten quivers and the tilting theory of the
finite dimensional algebras with discrete
derived categories. If time permits, we will give some
results about the classification of
t-structures of discrete derived categories.
Main references:
1. G. Bobinski, C. Geiss, and A.
Skowronski. Classification of discrete derived categories. Cent.
Eur. J. Math., 2(1):19–49 , 2004
2. N. Broomhead, D. Pauksztello, and D.
Ploog. Discrete derived categories I: Homomorphisms,
autoequivalences and t-structures.
arXiv:1312.5203.
3. C. Geiss, On Components of type
ZA\doubleinfty for string algebras, Comm. Algebra,26(3)
749-758,1998.
4. D. Vossieck. The algebras with discrete
derived category. J. Algebra, 243(1):168–176, 2001.
7.24-30 Dr. Zhi-Wei Li (Jiangsu Normal
Univ.)
6.21 Prof. Dr. Guodong Zhou (ECNU)
Title: A trichotomy theorem for adjoint sequences of triangle functors
Time: 06.21, 16:00-17:00
Location:
Abstract: In this talk we present a trichotomy theorem for adjoint
sequences of triangle functors between
compactly
generated triangulated categories such that their full subcategories of compact
objects admit
Serre
functors. As an application, we show that a Gorenstein triangular matrix
algebra induces an
unbounded
ladder. This talk is based on a joint work with P. Zhang, Y. H. Zhang and L.
Zhu.
5.31-6.4 Dr. Zhengfang Wang
(Paris 7)
Title:
Singular Hochschild cohomology and Gerstenhaber algebra
Time: 06.02, 10:00-11:00
Location:
Abstract: Let A be an associative algebra over a commutative ring k
such that A is projective as a k-module.
Then the
Hochschild cohomology HH^m(A, A) can be viewed as the Hom-space
Hom_{D^b(A\otimes_k A^{op})}(A, A[m])
in the
bounded derived category D^b(A\otimes_k A^{op}). We replace D^b(A\otimes_k
A^{op}) by the singular category
D_{sg}(A\otimes_k A^{op}), which is the
Verdier quotient of D^b(A\otimes_k A^{op}) by the full subcategory
Perf(A\otimes_k
A^{op}) consisting of perfect complexes of A\otimes_k A^{op}-modules and
define the singular
Hochschild cohomology HH_{sg}^m(A, A) to
be the Hom-space Hom_{D_{sg}(A\otimes_k A^{op})}(A, A[m]) for any
integer m.
In this
talk, we prove that HH_{sg}^*(A, A) has a Gerstenhaber algebra structure. We
provide a prop interpretation for this
Gerstenhaber
algebra (a joint work with G. Zhou). We will also give several examples
on how to compute HH_{sg}^*(A, A)
in the
case of radical square zero algebras A.
3.1-3.12 Dr. Dirk Kussin (Univ. Paderborn)
Title:
Noncommutative smooth projective cuvers
Time: 03.02,03,11, 14:00-15:00
Location:
1.8-1.14 Prof. Dr. Zhe Han
(Henan Univ.)
2015
12.25-12.29 Prof. Dr. Yanan Lin (Xiamen Univ.)
Title: A
mini-course on tubular algebras
Time: 12.26, 27, 28, 29, 9:30-11:30
Location:
12.25-12.29 Prof. Dr. Jianmin Chen (Xiamen Univ.)
11.12-11.14 Prof. Dr. Chao Zhang (Guizhou Univ.)
Title: On
the derived representation type of finite-dimensional algebras
Time: 11.13, 10:00-11:00
Location:
Abstract: In this talk, we will introduce some numerical invariants including cohomological length,
cohomological width, and cohomological range of a complex. The cohomological range leads to the concepts of derived bounded algebra and strongly derived unbounded algebra. Then we will describe the Brauer-Thrall type theorems for the bounded derived category of a finite-dimensional algebra. Moreover, we characterize the strongly derived unbounded algebra $A$ via the category $C_m(\proj A)$ and also the repetitive algebra $\hat{A}$, which provides a proof of the dichotomy on the representation type of $C_m(\proj A)$ and $\hat{A}$. 11.2-11.4 Prof. Dr. Jianmin Chen (Xiamen Univ.)
10.26-10.30 Dr. Dawei Shen (ECNU)
9.24-9.25 Dr. Zhi-Wei Li (Jiangsu Normal
Univ.)
9.25-9.26 Dr. Zhe Han (Henan Univ.)
9.23-9.26 Prof. Dr. Henning
Krause (Univ. Bielefeld, Bielefeld)
Title:
Highest weight categories and recollements
Time: 9.24, 15:00-16:00
Location:
Abstract: Highest weight categories and quasi-hereditary algebras arise naturally
in representation theory and were introduced in a series of papers by Cline, Parshall, and Scott. In my talk I provide several equivalent descriptions of a highest weight category using recollements of abelian categories. Also, I'll explain the connection between sequences of standard and exceptional objects
Note: there will be an informal half-day
algebra seminar on 9.25, 10:00-12:00 in 1518.
9.23-9.26 Dr. Shiquan Ruan (Tsinghua Univ.)
7.12-7.26 Prof. Dr. Shiping Liu (Univ. Sherbrooke)
Title: Covering
theory for linear categories with application to derived category
Time: 7.13, 15, 17, 20, 22, 24, 10:00-11:00
Location:
Abstract: We extend the Galois covering theory
introduced by Bongartz–Gabriel for skeletal
linear categories to general linear
categories. We show that a Galois covering between
Krull–Schmidt categories preserves
irreducible morphisms and almost splits sequences.
Specializing to derived categories, we
study when a Galois covering between locally bounded
linear categories induces a Galois
covering between the bounded derived categories of
finite dimensional modules. As an
application, we show that each locally bounded linear category
with radical squared zero admits a gradable
Galois covering, which induces a Galois covering
between the bounded derived categories of
finite dimensional modules, and a Galois covering
between the Auslander–Reiten quivers
of these bounded derived categories. In a future paper,
this will enable us to obtain a complete
description of the bounded derived category of finite
dimensional modules over a finite
dimensional algebra with radical squared zero.
5.18-5.22
Prof. Dr. Changchang Xi
(Capital Normal Univ.)
Title:
Dominant dimensions and tilting modules
Time:
5.19/20, 16:00-17:00
Location:
Abstract: This is a series of lectures on
dominant dimensions and tilting modules. We first recall
some basic results on the
subjects, and then present some new advances in this direction. The
motivation for this
consideration is to understand the famous Nakayama conjecture, which says
that algebras of infinity dominant
dimension should be quasi-Frobenius algebras, in the context
of derived categories. Most of
the contents of the lectures are taken from a joint paper with H. X. Chen.
4.17-4.18
Prof. Dr. Zhaoyong Huang
(Nanjing Univ.)
Title: Homological Aspects of the (Adjiont)
Cotranspose
Time:
4.18, 16:00-17:00
Location:
Abstract: As a dual of the Auslander transpose of modules, we introduce
and study the
cotranspose of modules and its
adjoint version
with respect to a semidualizing module.
3.30-4.09 Prof. Dr. Hagen Meltzer
(Univ. Szczecin)
Title: A
Mini-Course on Weighted Projective Line
Time:
4.01, 02, 03, 07, 08, 16:00-17:00
Location:
Abstract: click here for the
abstract for the five talks.
3.10-3.12 Dr. Zhi-Wei Li (Jiangsu Normal
Univ.)
Title:
Complete cotorsion pairs in exact categories
Time:
3.11, 16:30-17:30
Location:
Abstract: We discuss a
generalized version of Quillen's small object argument in arbitrary
categories. We use it to give a criterion
for the construction of complete cotorsion pairs
in arbitrary exact categories, which is a
generalization of the recent result due to Saorin
and Stovicek. This criterion also allows
us to recover Gillespie's recent work on the relative
derived categories of Grothendieck
categories.
1.27-1.31 Prof. Dr. Jiwei He (Shaoxing
Univ.)
Title: On
primitive ideals of symplectic algebras
Time:
1.28, 16:30-17:30
Location:
Abstract: In noncommutative algebra, primitive ideals play the role
as the maximal ideals in
commutative algebra. The set of all
primitive ideals in a noncommutative algebra A is usually called
the primitive spectrum of A. It is a
noncommutative analogue to the prime spectrum of a commutative
algebra. In this talk, I will give a
brief introduction to the primitive ideals of symplectic algebras.
The talk is based on Ginzburg's paper: On
primitive ideals, Selecta Math. New Series 9 (2003), 379-407.
1.11-1.13 Dr. Ming Lu (Sichuan Univ.)
Title: Singularity categories of the cluster-tilted algebras
of finite type
Time:
1.12, 10:00-11:00
Location:
Abstract: We use the stable categories of some sel_njective
algebras to describe the singularity
categories of the cluster-tilted algebras
of Dynkin type. Furthermore, in this way, we settle the
problem of singularity equivalence
classi_cation of the cluster-tilted algebra of type A, D and E
respectively. As a generalization of the
structure of the cluster-tilted algebra of type A, we define
the gluing Nakayama algebra, and use
technique of recollement to describe its singularity category
clearly.
2014
11. 10-11. 12 Prof. Dr. Yinhuo Zhang (Univ.
Hasselt, Hasselt)
Title: PBW deformations of Koszul algebras over
a nonsemisimple ring
Time:
11.11, 16:00-17:00
Location:
Abstract: Let $B$ be a
generalized Koszul algebra over a finite dimensional algebra $S$.
We
construct a bimodule Koszul resolution of $B$ when the projective dimension
of $S_B$
equals 2. Using this we prove a Poincar\'{e}-Birkhoff-Witt (PBW) type theorem
for a deformation of a generalized Koszul
algebra. When the projective dimension
of $S_B$
is greater than 2, we construct bimodule Koszul resolutions for generalized
smash
product algebras obtained from braidings between finite dimensional algebras
and Koszul
algebras, and then prove the PBW type theorem. The results obtained
can be
applied to standard Koszul Artin-Schelter Gorenstein algebras in the sense of
Minamoto
and Mori.
10.24-10.24 Prof. Dr. Pu Zhang
(Shanghai Jiaotong Univ.,
Title: Categorical resolutions of triangulated
categories
Time:
10.24, 15:30-17:30
Location:
Abstract: Categorical resolutions of a triangulated category come from looking
for a minimal resolution of singularities
of an algebraic variety. There are now
several definitions of a categorical
resolution of a triangulated category, mainly given
by A. Bondal and D. Orlov, A. Kuznetsov, M.
Van den Bergh, and V.A. Lunts. In this
talk, we will briefly recall their ways.By
using representation theory of Artin algebras
and the relative derived category, we will
give categorical resolutions of a class of
bounded derived categories, both in the
sense of A. Bondal and D. Orlov, and in
the sense of A. Kuznetsov. In the
commutative local Gorenstein case, this is also
in the sense of M. Van den Bergh.
06.05-06.09 Zhenqiang Zhou (Xiamen Univ., Xiamen)
06.05-06.09 Shiquan Ruan (Xiamen Univ., Xiamen)
05.01-05.06 Dr. Jianmin Chen (Xiamen Univ., Xiamen)
Title: Elliptic curves and weighted projective
lines of tubular type
Time:
05.05, 15:00-16:00
Location:
Abstract: Weighted projective lines have been widely
studied in the representation
theory of algebras. By computing the
genus, all the weighted projective lines can
be divided into three types: domestic,
tubular and wild. Among them, there is close
relationship between weighted projective
lines of tubular type and elliptic curves.
In this talk, we will recall the notions of
weighted projective lines and elliptic curves,
and then show the relationship between them
by an explicit example.
05.01-05.06 Zhenqiang Zhou (Xiamen Univ., Xiamen)
2013
07.23-07.29 Shiquan Ruan (Xiamen Univ.,
Xiamen)
07.20-07.25 Prof. Dr. Roozbeh Hazrat
(Univ. Western Sydney, Sydney)
Title: Graph algebras (I, II, III)
Time: 07.22,23,24, 16:00-17:00
Location:
Abstract: From a graph (e.g., cities and flights
between them) one can generate
an algebra which captures the movements
along the graph.
This talk is about one type of such
correspondences, i.e., Leavitt path algebras.
Despite being introduced only 8 years ago,
Leavitt path algebras have arisen
in a variety of different contexts as
diverse as analysis, symbolic dynamics,
noncommutative geometry and representation
theory. In fact, Leavitt path
algebras are algebraic counterpart to graph
C*-algebras. There are strikingly
parallel similarities between these two
theories. Even more surprisingly,
one cannot (yet) obtain the results in one
theory as a consequence of the other;
the statements look the same, however the
techniques to prove them are quite
different (as the names suggest, one uses
Algebra and other Analysis).
These all suggest that there might be a
bridge between Algebra and Analysis
yet to be uncovered.
In this talk, we introduce Leavitt path
algebras and then try to understand
the behaviour and to classify them by means
of (graded) K-theory.
06.28-07.03 Prof. Dr. Henning
Krause (Univ. Bielefeld, Bielefeld)
Title: An introduction to functors and morphisms determined by objects (I, II)
Time: 06.30, 07.01, 10:00-11:00
Location:
Abstract: The concept of a functor or morphism determined by an object was
introduced by Maurice Auslander in 1978 as an attempt to generalise previous results (joint with Idun Reiten) on the existence of almost split sequences. It seems that for many years this fundamental contribution of Auslander was almost forgotten. So I will explain this circle of ideas and I will show that this concept is particularly useful for studying morphisms in triangulated categories.
Title: A categorification of generalised noncrossing partitions
Time: 07.02, 10:00-11:00
Location:
Abstract: How are representations of different
quivers (over a common base field)
related? I will explain a categorical
framework to answer this question.
It involves a category of generalised
Cartan lattices which is determined
by the combinatorics of generalised
noncrossing partitions.
06.16-06.23 Prof. Dr. Shiping Liu (Univ.
Title: Auslander-Reiten theory of a Krull Schmidt category (I, II, III)
Time:
06.18, 06.19, 06.21, 10:00-11:00
Location:
Abstract: We introduce the notion of an Auslander-Reiten sequence in a Krull-Schmidt category.
This unifies the notion of an almost split sequence in an abelian category and that of an Auslander-Reiten triangle in a triangulated category. We then define the Auslander-Reiten quiver of a Krull-Schmidt category and describe the shapes of its semi-stable components. The main result generalizes those for an artin algebra and specializes to an arbitrary triangulated categories, in particular to the derived category of bounded complexes of finitely generated modules over an artin algebra of finite global dimension. 2012
Title: A course on Leavitt path algebras (I, II, III, IV,V)
Time:
07.18, 16:00-17:30; 07.23, 16:00-17:30; 07.25, 14:00-15:30;
08.03, 16:00-17:30; 08.27,9:30-11:00;
09.03, 14:00-15:30
Location:
Title: A course on Leavitt path algebras (VI)
Time:
09.10, 14:00-15:30
Location:
Abstract: click here.
Title: The Bi-module problems
Time:
06.21, 16:15-17:15
Location:
Abstract: In this talk we define two algebraic
structures, namely Bi-module problems
and Bi-co-module problems, and their
representation categories.
06.20-22,
Title: Hall algebras over triangulated categories
Time:
06.28, 16:00-17:30
Location:
Title: Integral bases of quantum cluster algebras for affine valued quiver
Time:
06.29, 16:00-17:30
Location:
Abstract: click here.
06.20-06.22 Prof. Dr. Dr. Claus Micheal Ringel (
Title: How modules over artin algebras determine morphisms
Time:
06.21, 15:00-16:00
Location:
Time:
06.22, 14:30-15:30
Location:
Abstract: Let R be an artin algebra. In his
Philadelphia Notes (published in 1978),
Auslander showed that any homomorphism
between R-modules is right determined by an
R-module. This topic is also the theme of
the last chapter in the book
of Auslander, Reiten and
Smalo. But it seems that the
relevance of these
considerations has not yet found the
attention they deserve.
One reason seems to be the somewhat
misleading terminology, this will be
discussed in the first lecture where we
outline a direct approach. We will draw the
attention to the indecomposable direct
summands of the minimal right determiner of a
morphism. In particular, the role of its
projective direct summands is of great interest.
The second lecture will provide a detailed
analysis of those morphisms which are right
determined by a module without any non-zero
projective direct summand. Here we
encounter an intimate relationship to the
vanishing of Ext^2.
06.13-15, 20-22 Zhi-Wei Li (Shanghai Jiaotong
Univ., Shanghai)
05.15-16, 18-20, 23-26 Zhi-Wei Li (Shanghai Jiaotong Univ., Shanghai)
03.24-03.26 Zhi-Wei Li (Shanghai Jiaotong
Univ., Shanghai)
2011
09.23-09.25 Prof. Dr. Henning
Krause (Univ. Bielefeld, Bielefeld)
Title: A compactness result for modules over artin algebras
Time:
09.24, 15:30-16:30
Location:
Abstract: We discuss the relation between the Gabriel-Roiter measure and
the Ziegler spectrum of an artin algebra. Both concepts are powerful but at the same time sophisticated and somehow technical. We illustrate all this by a compactness result for the lattice of submodule closed subcategories which is a recent theorem of Ringel.
09.23-09.25 Zhi-Wei Li (Shanghai Jiaotong Univ.,
Shanghai)
09.23-09.25 Dr. Lingling Yao (
09.17-09.25 Dr. Fei Xu (Univ.
Title: Introduction to category algebras
Time:
09.19, 20, 22, 15:30-17:30
Location:
Abstract: click here.
08.20-08.26 Dr. Jianmin Chen (Xiamen Univ., Xiamen)
Title: Generic sheaves on elliptic curves
Time:
08.23, 16:30-17:30
Location:
Abstract: We study the category of coherent sheaves on an elliptic
curve, and determine all the generic
sheaves on the elliptic curve by
pointing out that the rational function
sheave is a generic sheaf of
slope infinity. The category of coherent
sheaves can be classified by
generic sheaves. We introduce an effective
method to construct
generic sheaves on an elliptic curve.
08.20-08.29 Shiquan Ruan (
08.07-08.13 Longgang Sun (
08.03-08.14 Zhi-Wei Li (Shanghai Jiaotong Univ.,
08.03-08.14 Dr. Guodong Zhou (Ecole Poly., Lausann)
Title: Quiver representations and tame algebras
Time:
08.08,09, 11, 12, 15:00-17:00
Location:
Abstract: click here.
06.25-06.30 Prof. Dr. Yunge Xu (
Title: On tame algebras and bocses
Time:
06.26, 27, 28, 29, 15:00-17:00
Location:
GuanLiKeYan Building, Room 1318
Abstract: Based on the notion of bocs and its reduction techniques,
we will talk about the well-known
Drozd’s Tame-Wild dichotomy
(i.e. a finite dimensional algebra over an
algebraically closed field
is either tame or wild, and not both), and
Crawley-Boevey theorem
(i.e. almost all modules over a finite
dimensional tame algebra lie
in homogeneous tubes).
06.15-06.22 Prof. Dr. Weiqiang Wang (Univ.
Title: What is Schur duality?
Time:
06.17, 15:00-17:00
Location:
Abstract: Schur duality concerns about the interaction among general linear
Lie group/algebra, symmetric group, and
algebraic combinatorics. It
has generalizations to other classical Lie
groups, Lie superalgebras,
quantum groups, as well as to modular
representation theory in
prime characteristic.
Title: What is Boson-Fermion correspondence?
Time:
06.20, 15:00-17:00
Location:
Abstract: Boson-Fermion (B-F) correspondence has deep root in mathematical
physics. To us, the B-F correspondence is an interaction
between an
(infinite-dimensional)
Heisenberg algebra and Clifford algebra,
which categorifies the Jacob triple product
identity. The B-F
correspondence provides a new framework for
studying representation theory
of symmetric group and algebraic
combinatorics of symmetric
functions, and on the other hand, it is
also intimately related to
the integrable hierarchies of PDE.
Title: What is McKay correspondence?
Time:
06.21, 15:00-17:00
Location:
Abstract: McKay correspondence concerns a bijection between finite subgroups
of SL_2 and (affine) Dynkin diagrams of
simply-laced type, where the
Dynkin diagrams can be substituted by the
corresponding Lie
algebras/groups. The connection among these
will be made in a multiple
of ways, algebraic and geometric, via
finite group representations,
resolution of simple singularities, quiver
varieties, and
generalized symmetric groups.
05.15-05.29 Prof. Dr. Helmut Lenzing (Univ.
Title: Weighted projective lines and applications
Time:
05.17, 18, 20, 21, 26, 27, 15:00-16:00
Location:
Abstract: 1. Definition and basic properties
2. The role of the Euler characteristic
3. Classification aspects for zero or
negative Euler characteristic
4. Vector bundles and (graded)
Cohen-Macaulay modules
5. Stable categories of vector bundles (I)
6. Stable categories of vector bundles (II)
05.16-05.22 Dr. Lidan Tang (
05.16-05.28 Shiquan Ruan (
05.16-05.22 Jinjing Chen (
05.16-05.20 Prof. Dr. Libin Li (
04.20-04.25 Prof. Dr. Jiwei He (
Title: Introduction to Koszul and A-infinity algebras
Time:
04.21,22,24,25, 15:30-16:30
Location:
Abstract: 1. Basic properties of A-infinity algebras.
2. Koszul algebras and deformations.
3. AS-regular algebras and BGG
correspondence.
4. Potentials and Calabi-Yau property.
04.01-04.04 Dr. Lingling Yao (
04.01-04.02 Prof. Dr. Jun Wu (Anhui Normal Univ.,
Wuhu)
03.24-03.27 Dr. Nan Gao (
Title:
Stable t-structures and homotopy category
of Gorenstein-projective modules
Time:
03.25, 15:15-16:15
Location:
Abstract: We study the homotopy category of unbounded complexes of
Gorenstein-projective modules with bounded
relative homologies.
We show the existence of a right
recollement of these homotopy
categories. We show that the bounded
Gorenstein derived category of
a CM-finite Gorenstein artin algebra is triangle
equivalent to the bounded
derived category of an artin algebra.
03.24-03.27 Dr. Ning Bian (
Title:
Periodic two d-Koszul algebras
Time:
03.25, 16:30-17:30
Location:
Abstract: A d-Koszul algebra is said to be periodic if it has a periodic
minimal projective resolution. We will show
for a periodic two d-Koszul
algebra, its even Ext-algebra has global
dimension one. Using our previous
result, we prove that finitely generated
d-Koszul modules over a periodic
two d-Koszul algebra have rational
Poincar\'{e} series.
02.28-06.30 Huanhuan Li (Wubei Univ., Wuhan)
02.28-06.30 Ren Wang (Wubei Univ., Wuhan)
02.18-02.20 Longgang Sun (
2010
12.27-01.02 Prof. Dr. Yanhua Wang (
Title:
Constructing bi-Frobenius algebras via Yoneda algebras of AS-regular
algebras
Time:
12.29, 16:30-17:30
Location:
Abstract: Let E be an algebra with n generators and n generating relations. We construct a class
of bi-Frobenius algebras on the algebra E. For the cases n=2 and n=3, it is the Yoneda algebra of some AS-regular algebra of global dimension 3.
11.18-11.21
Prof. Dr. Dr. Claus
Micheal Ringel (Bielefeld)
Title:
Categorification
of the Fibonacci Numbers Using Representations of Quivers
Time:
11.18, 16:30-17:30
Location:
Abstract: It is well-known that the dimension vectors
of some relevant classes of indecomposable
representations of the
3-Kronecker quiver are pairs of Fibonacci numbers. We want to show in which
way the representations theory
of the 3-Kronecker quiver can be used in order to categorify properties
of Fibonacci numbers. The
different behaviour of even index and odd index Fibonacci numbers
will be illuminated in this way. In particular, we will present some joint
investigations with Philipp
Fahr which use the 3-Kronecker
quiver and its universal covering, the 3-regular tree, in order to
derive new partition formulas
for the Fibonacci numbers.