Computational Workshop on Singularities and Invariants Defined by Frobenius

Frobenius 定义的奇点和不变量计算研讨会

• 批准号: 1160927
• 负责人: Wenliang Zhang
• 金额: $ 1万
• 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: 2012
• 资助国家: 美国
• 起止时间: 2012-03-01 至 2013-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1160927&HistoricalAwards=false
• 关键词: Computational; Workshop; Singularities; Invariants; Defined

The singularities and numerical invariants defined via the Frobenius endomorphism are important to Commutative Algebra and Algebraic Geometry in prime characteristic. Since the introduction of tight closure theory and the discovery of the connection between singularities in prime characteristic and those arising from the Minimal Model Program, there has been an extensive theoretical study of these invariants; however, explicit computational examples of these invariants are rare. During this workshop, there will be introductory lecture series on tight closure, Hilbert-Kunz multiplicity, and test ideals, given by leading experts. Additionally, there will be a number of research talks on relevant existing computations of these and other topics. There also will be a session on using the computer algebra system Macaulay2 in the computation of these invariants, as well as a moderated open problem session during the conference.This workshop aims at bringing experts together to compute new and interesting classes of examples; identifying new connections between the measures arising in different contexts, especially numerical relations and bounds; and exposing graduate students, young researchers and even some undergraduate students to simple yet fundamentally important research questions that they can easily get their hands on.This workshop will take place at the University of Michigan, Ann Arbor, May 29th--June 1st, 2012. The organizing committee consists of: Karl Schwede (Pennsylvania State University), Kevin Tucker (Princeton University), and Wenliang Zhang (University of Michigan). More information can be found on the conference website: http://sites.google.com/site/computingfinvariantsworkshop/

由Frobenius自同态定义的奇点和数值不变量在交换代数和代数几何中具有重要的素特征。自从紧闭包理论的引入和发现了素数特征中的奇点与最小模型程序中的奇点之间的联系以来，人们对这些不变量进行了广泛的理论研究;然而，这些不变量的显式计算实例很少。在这次研讨会期间，将有介绍性的系列讲座紧闭，希尔伯特-昆兹多重性，并测试理想，由领先的专家。此外，将有一些关于这些和其他主题的相关现有计算的研究会谈。会议期间还将举行一次关于使用计算机代数系统Macaulay 2计算这些不变量的会议，以及一次主持的开放性问题会议。这次讲习班的目的是将专家聚集在一起计算新的和有趣的例子;确定不同情况下产生的度量之间的新联系，特别是数值关系和界限;并让研究生，年轻的研究人员，甚至一些本科生接触简单但根本重要的研究问题，他们可以很容易地掌握。这个研讨会将于2012年5月29日-6月1日在密歇根大学安阿伯举行。组委会成员包括：卡尔·施韦德（宾夕法尼亚州立大学）、凯文·塔克（普林斯顿大学）和张文良（密歇根大学）。更多信息可以在会议网站上找到：http://sites.google.com/site/computingfinvariantsworkshop/