Conference Proposal: Interactions between Representation Theory, Algebraic Topology and Commutative Algebra

2015年春季学期，一项研究项目将在西班牙巴塞罗那的马泰马蒂卡研究中心(CRM)举行。重点将放在表示论、代数拓扑学和交换代数之间的交集上。交换代数与代数拓扑学、交换代数与表示论之间的相互作用有着悠久的传统。在一个领域中出现和发展的技术和概念推动了另一个领域的发展。遗憾的是，建立和促进这三个学科(或其中任何两个)的合作的机会太少了，特别是在研究生和年轻研究人员之间，特别是在美国。过去十年，这三个学科经历了显著的变化和发展，CRM项目来得正是时候。NSF的这一奖项将资助美国机构的年轻研究人员(研究生、新近获得博士学位和初级教员)参加该计划的一些关键活动。这将为他们提供一个独特的机会来了解这些领域的当前研究以及领域之间的相互作用；彼此讨论想法，并开始就未来的研究进行合作。CRM计划将涵盖的主题，特别是高级课程和研讨会：矩阵因式分解，最大Cohen-Macaulay模；簇代数和簇范畴；支持变种的上同调理论；以及倾斜理论，仅举几例，是几个重要的和快速发展的数学领域的交叉，每个学科都从其他领域的进步中受益。客户关系管理计划将把这些学科的领先研究人员聚集在一起，人们可以乐观地认为，这将导致对它们的新见解和发展。该计划的亮点包括两个为期一周的高级课程，一个在2015年2月，题为交换代数和表示理论中的(重新)新兴方法，另一个在2015年4月，名为在代数和拓扑学之间建立桥梁。每次会议结束后，都将举行为期一周的研讨会。此外，还计划于2015年5月25日至29日举行一次会议。

A research program is to be held at the Centre de Recerca Matematica (CRM) in Barcelona, Spain in the Spring semester of 2015. The focus will be on the intersection between representation theory, algebraic topology, and commutative algebra. There is a long tradition of interaction between commutative algebra and algebraic topology, and commutative algebra and representation theory. Techniques and concepts that arose and were developed in one field have driven developments in the other. Regrettably, opportunities for building and fostering collaborations, especially among graduate students and younger researchers, from the three subjects (or indeed any two of them) have been all too rare, especially in the U.S. The three subjects have witnessed remarkable changes and developments in the last decade, and the CRM program comes at an opportune moment. This NSF award will fund the travel of younger researchers (graduate students, recent PhDs, and junior faculty) at U.S. institutions to participate in some of the key events of the program. This will provide them with a unique opportunity to learn about current research in these fields and the interactions between fields; discuss ideas with one another, and begin collaborations on future research.The topics to be covered by the CRM program, and in particular the advanced courses and workshops: matrix factorizations, maximal Cohen-Macaulay modules; cluster algebras and cluster categories; cohomological theory of support varieties; and tilting theory, to name a few, are at the intersection of several important and rapidly developing areas of mathematics, each subject benefitting from advances in the others. The CRM program will bring together leading researchers in each of these subjects, and one can be optimistic that this will lead to the new insights and developments in them. The highlights of the program include two, week-long, advanced courses, one in February 2015, titled (Re)emerging methods in Commutative Algebra and Representation Theory, and another in April 2015, titled Building bridges between Algebra and Topology. Each will be followed by a week-long workshop. Additionally, a conference is scheduled for 25--29th May, 2015.