NSF/CBMS Regional Conference in Mathematical Sciences--'Cluster Algebras and Applications'-6/13-17/2006

NSF/CBMS 数学科学区域会议——“簇代数及其应用”-6/13-17/2006

• 批准号: 0532631
• 负责人: Naihuan Jing
• 金额: $ 3.39万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-01-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0532631&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

The interaction between quiver representations and Lie theory has sparkled several important developments in mathematics, for instance Lusztig's introduction of canonical basis for quantum enveloping algebras in early 90's. Recently S. Fomin and A. Zelevinsky introduced a new algebraic structure called the cluster algebra in order to study positivity properties for canonical basis. This new algebraic structure has quicklyfound connections and applications in quiver theory, discrete dynamical systems, thermodynamic Bethe Ansatz, generalized associahedra Grassmannians, projective configurations, Poisson geometry and Teichmueller theory, and the quantum cluster algebra is also introduced and studied actively. In order to make this new area of research accessible to a wide audience we are holding an NSF/CBMS regional conference on ClusterAlgebras and their Applications at North Carolina State University in Raleigh during June 13--17, 2006 with Professor Zelvinsky as the principal speaker. The audience will have a chance to listen to one of the founders of cluster algebras to present the fundamental materials of cluster algebras. The lectures aim to introduce graduatestudents and new comers to the field. Specifically the following topics will be covered:1) Motivation--total positivity, canonical bases, double Bruhat cells;2) Definitions and first examples of cluster algebras;3) The Laurent phenomenon; 4) Rank 2 cluster algebras;5) Y-systems and generalized associahedra;6) Quantum cluster algebras;7) Cluster algebras and quiver representations.In order for an even wider audience to study the subjects the lecture notes of Professor Zelevinsky will be published by CBMS within one year after the conference. Graduate students and young researchers, in particular those from under-presented groups (women, minorities, and persons with disabilities) are strongly encouraged to attend the conference.

颤抖表示和李理论之间的相互作用引发了数学领域的一些重要发展，例如 Lusztig 在 90 年代初引入了量子包络代数的规范基础。最近，S. Fomin 和 A. Zelevinsky 引入了一种新的代数结构，称为簇代数，以研究规范基的正性性质。这种新的代数结构很快在箭袋理论、离散动力系统、热力学Bethe Ansatz、广义关联面体格拉斯曼、射影构型、泊松几何和Teichmueller理论中找到了联系和应用，并且量子簇代数也被积极地引入和研究。 为了使这一新的研究领域为广大受众所了解，我们将于 2006 年 6 月 13 日至 17 日在位于罗利的北卡罗来纳州立大学举办 NSF/CBMS 集群代数及其应用区域会议，由 Zelvinsky 教授担任主要发言人。 观众将有机会聆听簇代数创始人之一介绍簇代数的基础材料。讲座旨在向研究生和新人介绍该领域。 具体来说，将涵盖以下主题：1）动机——总正性、规范基、双布鲁哈特细胞；2）簇代数的定义和第一个例子；3）洛朗现象； 4）二阶簇代数；5）Y系统和广义关联面体；6）量子簇代数；7）簇代数和箭袋表示。为了让更广泛的受众学习这些科目，Zelevinsky教授的讲义将出版会议结束后一年内由 CBMS 进行。 强烈鼓励研究生和年轻研究人员，特别是那些来自代表性不足的群体（妇女、少数民族和残疾人）参加会议。