Visitors List

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:  GuanLiKeYan Building, Room 1318

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:  GuanLiKeYan Building 1318

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:  GuanLiKeYan Building 1318

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

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:  GuanLiKeYan Building 1318

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:  GuanLiKeYan Building 1218

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:  GuanLiKeYan Building 1518

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:  GuanLiKeYan Building 1518

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:  GuanLiKeYan Building 1518

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:  GuanLiKeYan Building 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

9.24-30   Dr. Huanhuan Li (West. Sydney Univ.)

Time: 9.25, 27, 10:30-11:30

Location:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1318

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1208

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1308

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1318

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

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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.)

Time:  1.12, 10:00-11:00

Location:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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., Shanghai)

Title:  Categorical resolutions of triangulated categories

Time:  10.24, 15:30-17:30

Location:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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:  GuanLiKeYan Building, Room 1518

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. Sherbrooke, Sherbrooke)

Title:  Auslander-Reiten theory of a Krull Schmidt category (I, II, III)

Time:  06.18, 06.19, 06.21, 10:00-11:00

Location:  GuanLiKeYan Building, Room 1518

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

07.16-09.18   Prof. Dr. Gonzalo Aranda Pino (Malaga)

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:  GuanLiKeYan Building, Room 1308


Title:  A course on Leavitt path algebras (VI)

Time:  09.10, 14:00-15:30

Location:  GuanLiKeYan Building, Room 1518

06.21-22      Prof. Dr. Yingbo Zhang (Beijing Normal Univ., Beijing)

Title:  The Bi-module problems

Time:  06.21, 16:15-17:15

Location:  GuanLiKeYan Building, Room 1518

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, 27-29  Prof. Dr. Xueqing Chen (Univ. Wisconsin-Whitewater)

Title:  Hall algebras over triangulated categories

Time:  06.28, 16:00-17:30

Location:  GuanLiKeYan Building, Room 1518

Title:  Integral bases of quantum cluster algebras for affine valued quiver

Time:  06.29, 16:00-17:30

Location:  GuanLiKeYan Building, Room 1518

06.20-06.22   Prof. Dr. Dr. Claus Micheal Ringel (Bielefeld)

Title:  How modules over artin algebras determine morphisms

Time:  06.21, 15:00-16:00

Location:  GuanLiKeYan Building, Room 1518

Time:  06.22, 14:30-15:30

Location:  GuanLiKeYan Building, Room 1208

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:  GuanLiKeYan Building, Room 1418

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 (Eastsouth Univ., Nanjing)

09.17-09.25  Dr. Fei Xu (Univ. Barcelona, Barcelona)

Title:  Introduction to category algebras

Time:  09.19, 20, 22, 15:30-17:30

Location:  GuanLiKeYan Building, Room 1518

08.20-08.26  Dr. Jianmin Chen (Xiamen Univ., Xiamen)

Title:  Generic sheaves on elliptic curves

Time:  08.23, 16:30-17:30

Location:  GuanLiKeYan Building, Room 1318

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 (Xiamen Univ., Xiamen)

08.07-08.13  Longgang Sun (Zhejiang Univ., Hangzhou)

08.03-08.14  Zhi-Wei Li (Shanghai Jiaotong Univ., Shanghai)

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:  GuanLiKeYan Building, Room 1318

07.27-08.05  Prof. Dr. Yanhua Wang (Shanghai)

06.25-06.30  Prof. Dr. Yunge Xu (Hubei Univ., Wuhan)

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. Virginia, Virginia)

Title:  What is Schur duality?

Time:  06.17, 15:00-17:00

Location:  GuanLiKeYan Building, Room 1611

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:  GuanLiKeYan Building, Room 1611

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:  GuanLiKeYan Building, Room 1611

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.

Time:  05.17, 18, 20, 21, 26, 27, 15:00-16:00

Location:  GuanLiKeYan Building, Room 1518

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 (Fuzhou Univ., Fuzhou)

05.16-05.28   Shiquan Ruan (Xiamen Univ., Xiamen)

05.16-05.22   Jinjing Chen (Xiamen Univ., Xiamen)

05.16-05.20  Prof. Dr. Libin Li (Yangzhou Univ., Yangzhou)

04.20-04.25  Prof. Dr. Jiwei He (Shaoxing Univ., Shaoxing)

Title:  Introduction to Koszul and A-infinity algebras

Time:  04.21,22,24,25, 15:30-16:30

Location:  GuanLiKeYan Building, Room 1518

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 (Eastsouth Univ., Nanjing)

04.01-04.02  Prof. Dr. Jun Wu (Anhui Normal Univ., Wuhu)

03.24-03.27  Dr. Nan Gao (Shanghai Univ., Shanghai)

Title:  Stable t-structures and homotopy category of Gorenstein-projective modules

Time:  03.25, 15:15-16:15

Location:  GuanLiKeYan Building, Room 1518

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 (Shandong Univ. Tech., Zibo)

Title:  Periodic two d-Koszul algebras

Time:  03.25, 16:30-17:30

Location:  GuanLiKeYan Building, Room 1518

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 (Zhejiang Univ., Hangzhou)

2010

12.27-01.02          Prof. Dr. Yanhua Wang (Shanghai)

Title:  Constructing bi-Frobenius algebras via Yoneda algebras of AS-regular algebras

Time:  12.29, 16:30-17:30

Location:  GuanLiKeYan Building, Room 1518

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:  KeYanGuanLi Building, Room 1518

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.