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

会议提案：表示论、代数拓扑学和交换代数之间的相互作用

• 批准号: 1501399
• 负责人: Srikanth Iyengar
• 金额: $ 3万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-02-01 至 2016-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1501399&HistoricalAwards=false
• 关键词: Conference; Proposal; Interactions; between; Representation

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.

2015年春季学期，将在西班牙巴塞罗那的De Recerca Matematica（CRM）举行一项研究计划。重点将放在代表理论，代数拓扑和交换代数之间的交集。交换代数和代数拓扑与交换代数和代表理论之间存在悠久的相互作用传统。在一个领域中出现和开发的技术和概念驱动了另一个领域的发展。遗憾的是，从三个主题（或实际上两个）中建立和促进合作的机会，尤其是在研究生和年轻的研究人员中，这太罕见了，尤其是在美国，这三个主题在过去十年中见证了这三个主题的重大变化和发展，CRM计划是在一个典型的时间。 NSF奖将资助美国机构的年轻研究人员（研究生，最近的博士学位和初级教师）的旅行，以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，以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计划涵盖的主题，尤其是高级课程和讲习班：矩阵因素化，最大的Cohen-Macaulay模块；集群代数和集群类别；支持品种的共同学理论；仅举几例，倾斜理论是在数学的几个重要且快速发展的领域的交汇处，每个主题都受益于其他主题。 CRM计划将在每个主题中汇集领先的研究人员，并且可以乐观，这将导致他们的新见解和发展。该计划的亮点包括两个，一周的高级课程，一门在2015年2月，标题为“通勤代数和代表理论”的（重新）新兴方法，而2015年4月另一项名为“代数和拓扑之间的建筑桥梁”。每个人都将举行为期一周的研讨会。此外，会议定于2015年5月25日至29日举行。