Commutative Algebra and its Interactions, July 31 - August 3, 2008

交换代数及其相互作用，2008年7月31日至8月3日

• 批准号: 0810844
• 负责人: Karen Smith
• 金额: $ 2.5万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0810844&HistoricalAwards=false
• 关键词: Commutative; Algebra; its; Interactions; July

ABSTRACT Principal Investigator: Smith, Karen E.Proposal Number: DMS - 0810844 Institution: University of Michigan Ann Arbor Title: Commutative Algebra and its InteractionsThis proposal is for a conference that will take place at the University of Michigan, Ann Arbor, July 31--August 5, 2008. The conference will focus on recent advances in commutative algebra, centered around areas which have been greatly influenced by the contributions of Mel Hochster. These include tight closure, singularities and multiplier ideals, the homological conjectures, invariant theory, local cohomology, the structure of free resolutions, and combinatorial commutative algebra. Hochster's research has had a transforming impact on the field, and there are several highly active areas which rely on his past and present work. We hope to bring together these areas for fruitful interaction. Commutative algebra is the study of equations: to paraphrase Hochster, "...algebra, after all, has to do with solving equations. Abstract algebra is the daughter of the theory of equations (in the broadest sense) and perhaps its best theorems still deal with that subject." Striking developments in the last few decades in commutative algebra have reinforced this view of commutative algebra. These developments include solutions to classical problems, as well as strengthened connections with diverse areas including algebraic topology, group cohomology, algebraic combinatorics, representation theory, invariant theory, and algebraic and arithmetic geometry. The invited speakers include experts in different areas, as well as several young researchers. The conference will provide an opportunity to present key results and recent advances. A special effort will be made to support the expenses of young researchers, women and minorities, graduate students, and those without alternative means of support.

摘要主要研究者：Smith，Karen E.提案编号：DMS - 0810844机构：密歇根大学安阿伯标题：交换代数及其相互作用本提案是为将于2008年7月31日至8月5日在密歇根大学安阿伯举行的会议提出的。会议将集中讨论交换代数的最新进展，围绕着梅尔·霍克斯特的贡献产生了很大影响的领域。这些包括紧闭包，奇点和乘子理想，同调代数，不变理论，局部上同调，自由决议的结构，和组合交换代数。Hochster的研究对该领域产生了变革性的影响，有几个高度活跃的领域依赖于他过去和现在的工作。我们希望将这些领域结合起来，进行富有成效的互动。交换代数是对方程的研究：套用Hochster的话，“......代数毕竟是解方程的。抽象代数是方程理论的女儿（在最广泛的意义上），也许它的最好的定理仍然处理这个问题。在过去的几十年里，交换代数的惊人发展加强了交换代数的这种观点。这些发展包括经典问题的解决方案，以及加强与不同领域的联系，包括代数拓扑，群上同调，代数组合学，表示论，不变理论，代数和算术几何。受邀的演讲者包括不同领域的专家，以及一些年轻的研究人员。会议将提供一个机会，介绍主要成果和最新进展。将作出特别努力，支持青年研究人员、妇女和少数民族、研究生以及没有其他支助手段的人的费用。