Two Half-Day Workshop:
Weighted Projective Lines
2022.7.1 &7.3,
USTC, Hefei, China
The aim of this
two half-day workshop is to promote academic communication between algebraists.
We will concentrate on weighted projective lines and related topic. The invited
speakers are encourage to present their own research or survey recent progress
on a specific topics in algebra.
Invited Speakers: Jianmin Chen (Xiamen), Yiyu Cheng (Hefei),
Jie Li (Hefei), Shiquan Ruan (Xiamen)
Program and Abstracts: TBA
All lectures will
take place at 1318 (Guanli Keyan Building).
Organizers:
Xiao-Wu Chen, Jue Le, Ren Wang, Yu Ye
Sponsors:
School of Math. Sci., NNSF, CAS
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