Computational Workshop on Singularities and Invariants Defined by Frobenius

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数特征。自从引入紧闭包理论，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，但这些不变量的显式计算实例很少。在这个工作坊期间，将有由知名专家讲授的关于紧闭包、希尔伯特-昆兹重数和检验理想的介绍性系列讲座。此外，还将举行一些关于这些主题和其他主题的相关现有计算的研究讲座。在会议期间，还将有一个关于在这些不变量的计算中使用计算机代数系统Macaulay2的课程，以及一个主持的开放问题课程。这个研讨会的目的是让专家们聚集在一起计算新的和有趣的例子类；识别不同背景下产生的度量之间的新联系，特别是数字关系和界限；并让研究生、年轻的研究人员甚至一些本科生接触到他们可以很容易获得的简单但基本重要的研究问题。这个研讨会将于2012年5月29日至6月1日在密歇根大学安娜堡举行。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)和张文亮(密歇根大学)。欲了解更多信息，请访问会议网站：http://sites.google.com/site/computingfinvariantsworkshop/。

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/