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

一个研究项目将于2015年春季学期在西班牙巴塞罗那的Centre de Recerca Matematica（CRM）举行。重点将放在表示论，代数拓扑和交换代数之间的交叉。交换代数与代数拓扑、交换代数与表示论之间的相互作用有着悠久的传统。在一个领域出现和发展的技术和概念推动了另一个领域的发展。令人遗憾的是，建立和促进合作的机会，特别是在研究生和年轻的研究人员中，从这三个主题（或其中任何两个）都太少了，特别是在美国，这三个主题在过去十年中见证了显着的变化和发展，CRM计划来得正是时候。该NSF奖项将资助美国机构的年轻研究人员（研究生，最近的博士生和初级教师）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，了解目前的研究在这些领域和领域之间的相互作用，讨论的想法与彼此，并开始合作对未来的研究。的主题将涵盖的CRM计划，特别是先进的课程和研讨会：矩阵因子分解，最大科恩-麦考利模;集群代数和集群类别;上同调理论的支持品种;和倾斜理论，仅举几例，是在几个重要的和迅速发展的数学领域的交叉点，每一个学科都受益于其他学科的进步。CRM计划将汇集这些学科的领先研究人员，人们可以乐观地认为，这将导致他们的新见解和发展。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（重新）新兴方法在交换代数和表示理论，另一个在2015年4月，题为代数和拓扑之间的桥梁。每次活动之后都将举办为期一周的研讨会。此外，会议定于2015年5月25日至29日举行。

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.