Commutative Algebra and Its Interactions with Algebraic Geometry

该奖项将为参加将于2015年7月7日至12日在密歇根大学安娜堡分校举行的“交换代数及其与代数几何的相互作用”会议的参与者，特别是初级研究人员和研究生提供支持。这次会议将有大量研究人员发表演讲，他们代表了广泛的资历水平和广泛的数学观点。会议将促进在主题领域发现新的联系，并鼓励新的互动和合作。它将为初级参与者提供一个极好的机会，让他们认识该领域的知名专家并向他们学习，并使他们自己的工作广为人知。被邀请的发言者名单非常强大，这将使会议能够吸引一大批不同的与会者。会议将集中讨论与紧闭包理论和与之相关的渐近数值不变量，如希尔伯特-昆兹重数和F-有理签名；与紧闭包理论相关的概念(例如，测试理想理论、由正特征方法定义的各种奇点和F-纯阈值)与定义在复数上的代数几何概念(例如，乘子理想理论、由几何方法定义的各种奇点和对数正则阈值)之间的相似以及许多相关问题。这些思想处于当代交换代数的前沿，如此大规模和有声望的会议创造了在悬而未决的问题上取得巨大进展的潜力，并发现了新的具有启发性的研究方向。

This award will provide support for participants, particularly junior researchers and graduate students, attending the conference "Commutative Algebra and Its Interactions with Algebraic Geometry," which will be held at the University of Michigan, Ann Arbor, during the period July 7-12, 2015. The conference will feature talks by a large number of researchers, representing a wide range of levels of seniority and a wide range of mathematical perspectives. The conference will foster the discovery of new connections in the theme fields and encourage new interactions and collaborations. It will provide an excellent opportunity for junior participants to meet and learn from established experts in the field, as well as to make their own work widely known. The extremely strong list of invited speakers will enable the conference to attract a large and diverse set of participants. The conference will focus on the explosive growth of ideas connected with tight closure theory and associated asymptotic numerical invariants like Hilbert-Kunz multiplicity and F-rational signature; the analogies between notions related to tight closure theory (e.g., the theory of test ideals, various kinds of singularities defined by positive characteristic methods, and F-pure thresholds) and notions defined in algebraic geometry over the complex numbers (e.g., the theory of multiplier ideals, various kinds of singularities defined by geometric methods, and log canonical thresholds); as well as many related questions. These ideas are on the cutting edge of contemporary commutative algebra and such a large and prestigious gathering creates the potential for dramatic progress on outstanding problems and the discovery of new and illuminating research directions.