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

主要研究者：Smith， Karen e .提案编号：DMS - 0810844机构：密歇根大学安娜堡分校题目：交换代数及其相互作用该提案将于2008年7月31日至8月5日在密歇根大学安娜堡分校举行的会议上提出。会议将集中讨论交换代数的最新进展，围绕Mel Hochster的贡献产生重大影响的领域。这些内容包括紧闭、奇点和乘子理想、同调猜想、不变理论、局部上同调、自由解的结构和组合交换代数。霍赫斯特的研究对该领域产生了革命性的影响，有几个高度活跃的领域依赖于他过去和现在的工作。我们希望把这些领域聚集在一起，进行富有成效的互动。交换代数是对方程的研究：套用霍克斯特的话来说，“……毕竟，代数与解方程有关。抽象代数是方程理论的女儿（在最广泛的意义上），也许它最好的定理仍然涉及这个主题。”在过去的几十年里，交换代数的惊人发展加强了对交换代数的这种看法。这些发展包括经典问题的解决方案，以及与不同领域的加强联系，包括代数拓扑、群上同调、代数组合、表示理论、不变理论以及代数和算术几何。受邀的演讲者包括不同领域的专家，以及几位年轻的研究人员。会议将提供机会介绍主要成果和最近的进展。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。

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.