Interactions between Commutative Algebra and Representation Theory

交换代数与表示论之间的相互作用

• 批准号: 1203469
• 负责人: Dan Zacharia
• 金额: $ 1.75万
• 依托单位: Syracuse University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1203469&HistoricalAwards=false
• 关键词: Interactions; between; Commutative; Algebra; Representation

Commutative algebra and representation theory are two flourishing areas of research in algebra. For commutative algebra, early on, its roots in algebraic geometry and number theory provided the major influences, while representation theory was partly motivated early on by problems in physics. More recently there has been significant interaction between these two areas. Some of this interaction goes back to the work of Auslander, his students and collaborators in the 1970s, but the last decade or so has seen a striking resurgence of new ideas and research in the overlap, as exemplified by recent work of Avramov, Buchweitz, Burban, Huneke, Iyama, Reiten and Yoshino, to name only a few.There have been relatively few joint meetings in the U.S. allowing researchers in commutative algebra and representation theory and their students to interact. It is vital to support the continued interactions between the areas by bringing together top researchers to report on their findings and to establish new cross disciplinary collaborations. Equally important is a gathering where recent doctorates, graduate students, and faculty from primarily teaching institutions can learn about recent developments and establish research connections with other workers across the two fields. To address these issues, the investigators plan a three-day conference at Syracuse University. The conference will take place on April 13-15, 2012. Leading researchers from both commutative algebra and representation theory will speak on their findings. Ample time for discussions will also be available to provide an opportunity for the participants, including the speakers, to establish new cross-collaborations. We intend to recruit an audience in which graduate students and recent doctorates are significantly represented. The URL for the conference is http://www.commalg.org/ROBfest/

交换代数和表示论是代数学中两个非常活跃的研究领域。 对于交换代数，早期，它在代数几何和数论中的根源提供了主要的影响，而表示论在早期部分受到物理问题的启发。 最近，这两个领域之间出现了重大互动。这种互动可以追溯到Auslander，他的学生和合作者在20世纪70年代的工作，但在过去的十年左右已经看到了新的想法和研究的重叠，如最近的工作Avramov，Buchweitz，Brban，Huneke，Iyama，Reiten和Yoshino，仅举几例。在uidoss，允许交换代数和表示论的研究人员及其学生进行互动的联席会议相对较少。通过汇集顶尖研究人员报告他们的发现并建立新的跨学科合作来支持各领域之间的持续互动至关重要。同样重要的是一个聚会，最近的博士，研究生和教师从主要教学机构可以了解最新的发展，并建立研究连接与其他工人在这两个领域。为了解决这些问题，研究人员计划在锡拉丘兹大学举行为期三天的会议。会议将于2012年4月13日至15日举行。来自交换代数和表示论的主要研究人员将谈论他们的发现。还将提供充足的讨论时间，为包括发言者在内的与会者提供建立新的交叉合作的机会。我们打算招募一个观众，其中研究生和最近的博士学位显着代表。会议的URL是http://www.commalg.org/ROBfest/