Recent Developments in Positive Characteristic Methods in Commutative Algebra: Frobenius Operators and Cartier Algebras

交换代数正特征方法的最新进展：Frobenius 算子和 Cartier 代数

• 批准号: 1507908
• 负责人: Yongwei Yao
• 金额: $ 2.45万
• 依托单位: Georgia State University Research Foundation, Inc.
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-02-15 至 2016-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1507908&HistoricalAwards=false
• 关键词: Recent; Developments; Positive; Characteristic; Methods

This award supports participation in the conference Recent Developments in Positive Characteristic Methods in Commutative Algebra, held during March 13-15, 2015, at Georgia State University, Atlanta, Georgia. The motivation behind the conference is to bring together researchers, including postdoctoral researchers and graduate students, in commutative algebra and related areas, in order to exchange ideas and discuss recent developments in positive characteristic methods. Top researchers in the field as well as postdocs and graduate students will be invited to speak at the conference. To make the conference accessible to all participants, introductory talks are scheduled. The conference will provide a platform for the participants to start exploring research aspects related to the highlighted topics, and it is anticipated that they will contribute research progress in these areas within a few years. More information can be found on the conference web site: http://www2.gsu.edu/~matfxe/gsu-usc/foca.htmlThe conference will focus on recent developments in positive characteristic methods. Research on positive characteristic methods has seen tremendous developments in recent years via using concepts related to the Frobenius homomorphisms. This includes the tight closure theory in characteristic p, singularities derived via tight closure theory, as well as the corresponding singularities in characteristic zero (via reduction to characteristic p) in algebraic geometry. The highlights of the conference, Frobenius operators and Cartier algebras, also involve the Frobenius homomorphisms in very fundamental ways. Both of them have intricate connections with the tight closure theory, birational geometry, F-modules, F-stability, test ideals, jumping numbers, anti-canonical covers, etcetera. Very recent research also includes the invariant "Frobenius complexity" being defined in order to measure whether a ring Frobenius operators is finitely generated. This conference will provide an opportunity for the participants to get exposed to the topics, exchange ideas, forge collaborations, and contribute to these research areas.

该奖项支持在交换代数中的正特征方法的最新发展会议的参与，在2015年3月13日至15日期间举行，在格鲁吉亚州立大学，亚特兰大，格鲁吉亚.会议背后的动机是汇集研究人员，包括博士后研究人员和研究生，在交换代数和相关领域，以交流思想和讨论积极的特征方法的最新发展。该领域的顶尖研究人员以及博士后和研究生将被邀请在会议上发言。为了使所有与会者都能参加会议，安排了介绍性发言。会议将为与会者提供一个平台，开始探索与突出主题相关的研究方面，预计他们将在几年内为这些领域的研究进展做出贡献。 更多的信息可以在会议网站上找到：http://www2.gsu.edu/~matfxe/gsu-usc/foca.htmlThe会议将集中在积极的特征方法的最新发展。近年来，正特征方法的研究由于引入了Frobenius同态的相关概念而得到了很大的发展。这包括特征p中的紧闭理论，通过紧闭理论导出的奇点，以及代数几何中特征零中的相应奇点（通过还原为特征p）。会议的亮点，弗罗贝纽斯算子和卡地亚代数，也涉及弗罗贝纽斯同态在非常基本的方式。它们都与紧闭包理论、双有理几何、F-模、F-稳定性、测试理想、跳跃数、反正则覆盖等有着千丝万缕的联系。最近的研究还包括定义不变的“Frobenius复杂度”，以衡量一个环Frobenius算子是否是非线性生成的。本次会议将为与会者提供一个机会，让他们接触到的主题，交流思想，建立合作，并为这些研究领域作出贡献。