Commutative Algebra and Its Interactions with Algebraic Geometry

该奖项将为参与者提供支持，特别是初级研究人员和研究生，参加会议“交换代数及其与代数几何的相互作用”，这将是在密歇根大学，安阿伯，在2015年7月7日至12日期间举行。会议将由大量的研究人员进行会谈，代表了广泛的资历和广泛的数学观点。 会议将促进发现主题领域的新联系，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，与该领域的知名专家见面和学习，并使他们自己的工作广为人知。邀请的发言者名单非常强大，将使会议能够吸引大量不同的与会者。会议将重点关注与紧闭包理论和相关的渐近数值不变量（如希尔伯特-昆兹多重性和F-有理数签名）相关的思想的爆炸性增长;与紧闭包理论相关的概念之间的类比（例如，测试理想的理论，由正特征方法定义的各种奇异性，以及F纯阈值）和在复数上的代数几何中定义的概念（例如，乘子理想的理论，由几何方法定义的各种奇点，和对数正则阈值）;以及许多相关的问题。 这些想法是在当代交换代数的前沿，这样一个大的和有声望的聚会创造了巨大的进展，对突出的问题和新的和有启发性的研究方向的发现的潜力。

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.