*Representation Day in USTC
(IV)*

2020.10.24 (Saturday),
Hefei, China

The aim of this
one-day workshop is to promote academic communication between

algebraists. We
are concentrated on the representation theory and related topics in

algebra. Invited
speakers are encourage to present their own research or survey recent

progress on a
specific topics in algebra

** Program**:

10:00-10:50 Yongjie Wang (Hefei Univ. Tech.)

11:00-11:50 Huanhuan Li (Anhui Univ.)

12:00-14:00
Lunch Break

14:00-14:50 Lei Du (Anhui Univ.)

15:00-15:50 Zhi Chen (Hefei Univ. Tech.)

All lectures will
take place at 1318 (Guanli Keyan Building).

** Abstracts**: available here.

** Organizers**:
Xiao-Wu Chen, Jue Le, Ren Wang, Yu Ye

** Sponsors**:
School of Math. Sci., NNSF, CAS

*Representation Day in USTC
(III)*

2013.7.24
(Wednesday),

** Program**:

9:30-10:30 Feng Wei (Beijing Institute
of Technology)

11:00-12:00 Shiquan Ruan (

12:00-14:30
Lunch Break

14:30-15:30 Yanhua Wang (

16:00-17:00 Roobeh Hazrat (Univerisy of

All lectures will
take place at

** Abstracts**:

Feng Wei, Ring-theoretic
properties of some noncommutative completed

algebras

*Abstract*: In this talk I will present the structure and ring-theoretic
properties

of some
non-commuttaive completed algebras. The involved algebras mainly

include Iwasawa
algebras, completed Hopf algebras and completed Weyl

algebras. Some
known results and open questions will be demonstrated.

Shiquan Ruan,
Tilting bundles and the ``missing part" on the weighted

projective line of
type (2, 2, n)

*Abstract*: We classify all the tilting bundles in the category of coherent

sheaves on the
weighted projective line of weight type (2, 2, n) , and

investigate the
abelianness of the ``missing part" from the category of

coherent sheaves
on weighted projective lines to the category of finitely

generated modules
on the endomorphism algebra for each tilting bundle.

Yanhua Wang, Hopf
actions on filtered regular algebras

*Abstract*: We study finite dimensional Hopf algebras actions on filtered

Artin-Schelter regular
algebras of dimension 2. Results on the Gorenstein

condition and on
the global dimension of the corresponding fixed subrings

are provided.

Roozbeh Hazrat,
Graph algebras

*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.

** Organizers**:
Xiao-Wu Chen, Jue Le, Yu Ye

** Arrival**: Take Bus No.10, 129 or 1 from the train
station to USTC (中国科学技术大学),

or take a taxi to USTC
(east campus, the cross of

which costs around
20 Yuan.

** Sponsors**:
School of Mathematical Sciences, Wu Wen-Tsun Key Lab. of Math., 985
Project,

NNSF, NECT

*Representation Day in USTC
(II)*

2011.4.2
(Saturday),

** Program**:

9:30-10:30 Hualin Huang (

11:00-12:00 Jiafeng Lv (

12:00-14:00 Lunch
Break

14:00-15:00 Can Zhu (

15:20-16:20 Xiaojin Zhang (

16:50-17:50 Zhaoyong Huang (

All lectures will
take place at

** Abstracts**:

Hualin Huang,
Monoidal structures on quiver representations

*Abstract*: We study possible monoidal structures, i.e., natural tensor products,
on the category of a

quiver.

Jiafeng Lv,
Introduction to piecewise-Koszul algebras

*Abstract*: In this talk, we will talk about piecewise-Koszul algebras, including

nonpure
piecewise-Koszul modules/algebras, weakly piecewise-Koszul modules,

quasi-piecewise-Koszul
modules/algebras and some applications.

Can Zhu, Hopf
actions on Calabi-Yau algebras

*Abstract*: For a graded automorphism
on a graded algebra or a Hopf action

on a graded
algebra, homological determinant is
defined, which is a generalization

of the usual
determinant of a matrix. By means of homological determinant, we

study the
Calabi-Yau property of smash product of a graded Calabi-Yau algebra

with a Hopf
algebra. This is joint with Wu Quanshui and Liu Liyu.

Xiaojin Zhang, Cluster tilting for tilted
algebras

*Abstract*: We build a connection
between iterated tilted algebras with trivial cluster tilting

and tilted
algebras of finite type. As a result, we can classify all tilted algebras with
cluster

tilting in terms
of quivers, that is, all tilted algebras with cluster tilting are of finite
type.

Moreover, we draw
the quivers of Auslander's 1-Gorenstein algebras with global dimension

2 admitting trivial
cluster tilting subcategories, which implies that such algebras are tilted

of finite type but
not Nakayama.

Zhaoyong Huang, Invariant properties of representations under (weak)
excellent extensions

*Abstract*: We introduce the notion of weak excellent extensions of rings as a
generalization of

that of excellent extensions of rings.
Let $S$ be a weak excellent extension of an Artinian

algebra $\Lambda$.
We prove that if $\Lambda$ is of finite representation type (resp.

CM-finite, CM-free),
then so is $S$; furthermore, if $S$ is an excellent extension of

$\Lambda$,
then the converse also holds true. We also study when the representation

dimension
of an Artinian algebra is invariant under excellent extensions.
It is a joint work

with Juxiang Sun.

** Organizers**:
Xiao-Wu Chen, Jue Le, Yu Ye

** Arrival**: Take Bus No.10, 129 or 1 from the train
station to USTC (中国科学技术大学),

or take a taxi to
USTC (east campus, the cross of

which costs around
20 Yuan.

** Accommodation**: All the invited speakers will stay at the USTC
guesthouse (专家楼),

which is near the
north door of our east campus. Participants who require accommodation

support should
email the organizers.

** Sponsors**:
Math. Department in USTC,Wu Wen-Tsun Key Lab. of Math., 985 Project,
NNSF, CAS

*Representation Day in USTC
(I)*

2010.11.20
(Saturday),

** Program**:

9:30-10:30 Jiwei He (

11:00-12:00 Jiaqun Wei (

12:00-14:00
Lunch Break

14:00-15:00 Yunge Xu (

15:20-16:20 Yanhong Bao (

16:50-17:50 Libin Li (

All lectures will
take place at

** Abstracts**:

Jiwei He,
Calabi-Yau property of filtered algebras

*Abstract*: We recall the definitions of Calabi-Yau algebra both in the sense of
Kontsevich

and of Ginzburg,
and then recall some relations of these two notions. We mainly focus

on the Calabi-Yau
property of filtered algebras: (i)
algebras with ascending positive

filtrations; (ii)
algebras with descending positive filtrations (the resulting topological

algebra is
complete). Among the class (i), we mainly discuss the Calabi-Yau property

of Sridharan
algebras; among the class (ii), we mainly discuss the Calabi-Yau property of

noetherian
complete algebras by means of coalgebras.

Jiaqun Wei,
Semi-tilting complexes

*Abstract*: We introduce the notion of semi-tilting complexes, which is a little
generalization

of tilting
complexes. Non-trivial semi-tilting complexes exist for any non-semisimple
non-local

artin algebras,
while tilting complexes may not. We extend interesting results in the tilting
theory

to semi-tilting
complexes. As corollaries, we also obtain some new characterizations of tilting

complexes.

Yunge Xu,
Hochschild cohomology of truncated quiver algebras

*Abstract*: For a truncated quiver algebra over a field of arbitrary
characteristic, we first calculate

its Hochschild
cohomology groups, and show that its Hochschild cohomology algebra is

finite-
dimensional iff its global dimension is finite iff its quiver has no oriented
cycles.

Moreover, based on
the minimal projective bimodule resolution, the Gerstenhaber bracket

products on the
Hochschild cohomology spaces for truncated quiver algebras are described

explicitly in
terms of the combinatorics of the quiver. As a consequence, for truncated basic
cycle

algebra A, each
element in HH^2(A) defines a noncommutative Poisson structure on A, and

in turn defines
the first multiplication of a one-parameter deformation of A.

Yanhong Bao, The
cohomology and deformation of Poisson algebras

*Abstract*: For a noncommutative Poisson algebra, we study its quasi-Poisson
cohomology,

and introduce its
Poisson complex and then its Poisson cohomology. The relation

between the
Poisson cohomology and the deformation theory of Poisson algebras

is discussed. This
is joint with Yu Ye.

Libin Li, Constructing indecomposable
representations over U_q(sl_2) via Ore extension

*Abstract*: In my talk, we shall discuss the infinite dimensional indecomposable representations

over U_q(sl(2))
via Ore extension. We obtain a class of infinite dimensional indecomposable

modules which are
not Harish-Chandra modules. This is a joint work with Zhihua Wang.

** Organizers**:
Xiao-Wu Chen, Jue Le, Yu Ye

** Arrival**: Take Bus No.10, 129 or 1 from the train
station to USTC (中国科学技术大学),

or take a taxi to
USTC (east campus, the cross of

which costs around
20 Yuan.

** Accommodation**: All the invited speakers will stay at the USTC
guesthouse (专家楼),

which is near the
north door of our east campus. Participants who require accommodation

support should
email the organizers.

** Sponsors**:
Math. Department in USTC, 985 Project, NNSF