2021 Workshop on Cluster Algebras and Related Topics

2021 Workshop on Cluster Algebras and Related Topics
2021-08-02
Online

Introduction:
Cluster algebra was introduced by Fomin and Zelevinsky at the beginning of this century, since then it has been proved to be related to various areas of mathematics, such as Combinatorics, Representation Theory of Algebras, Mathematical Physics, Poisson Geometry, Teichmuller Theory, algebraic geometry and many others. For examples, some important problems in this theory, including the conjecture on positivity of cluster variables and the problem on categorifications of cluster algebras, have being influenced the development of canonical bases of Lie theory and representation theories of quantum groups and KLR algebras, and etc.
Over the past years, many young scholars have entered this field. In order to make the young scholars have a better understanding of the frontiers and hot issues in this field, we plan to organize this workshop. Also, we will invite some most important leading experts in this fields to participate at this workshop such that the attending young scholars may communicate and exchange directly with these experts.
We hope this workshop can build a platform of high level for scholars in this field to exchange ideas and provide an opportunity for them to show mathematics each other. Finally, we hope to promote the further development of this subject via this workshop.
This workshop should be a platform of high level for scholars working at cluster algebras and related topics to show their results and exchange new ideas.
Based on the importance of cluster algebra theory in mathematics, we expect that this conference will promote the progress of some key issues in the frontier of mathematics and help young scholars to enter this meaningful field more quickly.

Time:  August 2-6, 2021
 
Organizers: 
Xueqing Chen (University of Wisconsin-Whitewaterchenx@uww.edu)
Fang Li (Zhejiang Universityfangli@zju.edu.cn)
Fan Qin (Shanghai Jiao Tong Universityqin.fan.math@gmail.com)
Linhui Shen (Michigan State Universitylinhui@math.msu.edu)
Bin Zhu (Tsinghua Universityzhu-b@mail.tsinghua.edu.cn)

Sponsors: 

Morningside Center of Mathematics, CAS


Online: 
Zoom ID: 466 356 2952   Password: mcm1234

Link: 

Schedule: 

August 2nd, 2021 (Monday)

7:50-8:00

Opening Ceremony

Recorded Content

8:00-8:50

Man-Wai Cheung
Chair: Xueqing Chen

Cluster varieties: compactification and holomorphic correspondence

PPT&Video

9:00-9:50

Daniel Labardini-Fragoso
Chair: Fan Qin

Laminations, tau-reduced components, generic bases and bangle bases

PPT&Video

10:00-10:50

Shiquan Ruan
Chair: Bin Zhu

Tilting objects on tubular weighted projective lines: a cluster tilting approach

PPT&Video

14:00-14:50

Jie Xiao
Chair: Quanshui Wu

The multiplication formulas of quantum cluster algebras (I)

PPT&Video

15:00-15:50

Fan Xu
Chair: Bin Zhu

The multiplication formulas of quantum cluster algebras (II)

PPT&Video

20:00-20:50

Haicheng Zhang
Chair: Fan Qin

Acyclic quantum cluster algebras via derived Hall algebras

PPT&Video

21:00-21:50

Daping Weng
Chair: Linhui Shen

Augmentations, Fillings, and Clusters of Positive Braid Closures

PPT&Video

22:00-22:50

Alexander Goncharov
Chair: Linhui Shen

Cluster structures on moduli spaces of non-commutative local systems on decorated surfaces

PPT&Video

August 3rd, 2021 (Tuesday)

8:00-8:50

Ralf Schiffler
Chair: Linhui Shen

On a geometric model for syzygies over 2-Calabi-Yau tilted algebras

PPT&Video

9:00-9:50

Yu Qiu
Chair: Bangming Deng

Calabi-Yau-X and cluster-X categories from decorated marked surfaces(=DMS)

PPT&Video

10:00-10:50

Yu Zhou
Chair: Bangming Deng

A geometric model for perfect categories of graded skew-gentle algebras

PPT&Video

14:00-14:50

Kyungyong Lee
Chair: Bernhard Keller

Greedy bases revisited, with a view toward the Jacobian conjecture

PPT&Video

15:00-15:50

Min Huang
Chair: Fang Li

Positivity for quantum cluster algebras from orbifolds

PPT&Video

20:00-20:50

Ben Davison
Chair: Pierre-Guy Plamondon

Strong positivity for quantum cluster algebras

PPT&Video

21:00-21:50

Travis Mandel
Chair: Fan Qin

Bracelet bases are theta bases

PPT&Video

22:00-22:50

Pierre-Guy Plamondon
Chair: Ben Davison

On g-vector fans of cluster algebras

PPT&Video

August 4th, 2021 (Wednesday)

8:00-8:50

Kiyoshi Igusa
Chair: Gordana Todorov

Duality of signed exceptional sequences

PPT&Video

9:00-9:50

Gordana Todorov
Chair: Kiyoshi Igusa

Semi-invariant pictures of tame hereditary algebras near their null roots

PPT&Video

10:00-10:50

Changjian Fu
Chair: Kyungyong Lee

c-vectors and f-vectors revisited

PPT&Video

August 5th, 2021 (Thursday)

8:00-8:50

Hiraku Nakajima
Chair: Jie Xiao

Representations of shifted Yangian

PPT&Video

9:00-9:50

Myungho Kim
Chair: Fan Qin

Cluster algebras and finite-dimensional modules over quantum affine algebras

PPT&Video

10:00-10:50

Peng Shan
Chair: Zhaobin Fan

Cohomology of affine Springer fibres and centre of small quantum groups

PPT&Video

14:00-14:50

Ming Fang
Chair: Libin Li

Rigidity dimension of algebras

PPT&Video

15:00-15:50

Nanqing Ding
Chair: Dingguo Wang

Recollements associated to cotorsion pairs over upper triangular matrix rings

PPT&Video

16:00-16:50

Yannan Qiu
Chair: Ming Fang

The based rings of two-sided cells in an affine Weyl group of type \tilde B_3

PPT&Video

20:00-20:50

Tomoki Nakanishi
Chair: Min Huang

Cluster patterns and scattering diagrams

PPT&Video

21:00-21:50

Jiarui Fei
Chair: Peigen Cao

Tropical F-polynomials and Cluster Algebras

PPT&Video

22:00-22:50

Peigen Cao
Chair: Lang Mou

Bongartz completion via c-vectors.

PPT&Video

August 6th, 2021 (Friday)

8:00-8:50

Osamu Iyama
Chair: Bin Zhu

Wall-chamber structure in Grothendieck group and canonical decomposition

PPT&Video

9:00-9:50

Li Li
Chair: Xueqing Chen

Support of elements in cluster algebras

PPT&Video

10:00-10:50

Song He
Chair: Fang Li

Cluster algebras for scattering amplitudes

PPT&Video

14:00-14:50

Quanshui Wu
Chair: Yang Han

A neralization of koszul algebra and koszul duality

PPT&Video

15:00-15:50

Karin Baur
Chair: Bin Zhu

Orbifold diagrams and skew group categories

PPT&Video

20:00-20:50

Xiuping Su
Chair: Xueqing Chen

Auslander algebras and cluster algebras C[G/P] in type A

PPT&Video

21:00-21:50

Matthew Pressland
Chair: Michael Shapiro

Categorification of positroid varieties

PPT&Video

22:00-22:50

Michael Shapiro
Chair: Matthew Pressland

Noncommutative cluster integrability

PPT&Video