Local Cohomology in Commutative Algebra and Algebraic Geometry

交换代数和代数几何中的局部上同调

基本信息

批准号：
1700748
负责人：
Christine Berkesch
金额：
$ 3万
依托单位：
University of Minnesota-Twin Cities
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-04-01 至 2018-03-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1700748&HistoricalAwards=false
关键词：
Local Cohomology Commutative Algebra Algebraic

项目摘要

This award supports participation in an international conference entitled Local Cohomology in Commutative Algebra and Algebraic Geometry, at the University of Minnesota on August 7 - 11, 2017. The topic of this meeting will be recent advances in Commutative Algebra related to local cohomology, rings of prime characteristic, D-modules, and the homological conjectures. The purpose of this conference is twofold. First, it will set up a platform where new collaborative research projects can be started, current ones can be furthered, and completed ones can be reported on. Second, the meeting will take advantage of the Midwest's outstanding tradition in commutative algebra and algebraic geometry and contribute to this tradition by giving young mathematicians an opportunity to meet the leaders in the field and absorb the latest trends and techniques. Through a poster session, this meeting will help, in particular, with the transition from graduate student to academic employee. We will also disseminate new results discussed at the conference though a bundled publication. The journal "Communications in Algebra" will publish a special volume dedicated to this meeting. The award will be used primarily to fund young mathematicians, graduate students and recent postdocs.The goal of this conference is to contribute to the training of scientists and to advance research in commutative algebra and algebraic geometry by bringing together students, postdoctoral fellows, and more senior international experts. Commutative algebra and algebraic geometry are vibrant fields with rich and ever evolving interconnections. Local cohomology possesses intriguing ties with other areas of mathematics such as D-modules, interactions with the Frobenius morphism, hypergeometric differential equations and their solution sheaves, singularity invariants based on the de Rham functor, and big Cohen--Macaulay algebras. Recent discoveries have occurred that touch finiteness properties, the cohomology of Milnor fibers, the homological conjectures, and birational geometry. This meeting will take advantage of these new developments and infuse them into the current generation of graduate students. Further information can be found at the conference website: http://www-users.math.umn.edu/~cberkesc/localCohomConf2017

该奖项支持参加 2017 年 8 月 7 日至 11 日在明尼苏达大学举行的名为“交换代数和代数几何中的局部上同调”的国际会议。本次会议的主题将是与局部上同调、环相关的交换代数的最新进展。素数特征、D-模和同调猜想。这次会议的目的是双重的。一是搭建新的合作研究项目的启动、现有的合作研究项目的深化、已完成的合作研究项目的汇报平台。其次，会议将利用中西部地区在交换代数和代数几何方面的杰出传统，并为年轻数学家提供与该领域的领导者会面并吸收最新趋势和技术的机会，从而为这一传统做出贡献。通过海报会议，这次会议将特别有助于从研究生到学术雇员的转变。我们还将通过捆绑出版物传播会议上讨论的新结果。《Communications in Algebra》杂志将出版本次会议的专刊。该奖项将主要用于资助年轻数学家、研究生和最近的博士后。本次会议的目标是通过聚集学生、博士后等人员，为科学家的培训做出贡献，并推进交换代数和代数几何的研究资深国际专家。交换代数和代数几何是充满活力的领域，具有丰富且不断发展的相互联系。局部上同调与其他数学领域有着有趣的联系，例如 D 模、与 Frobenius 态射的相互作用、超几何微分方程及其解滑轮、基于 de Rham 函子的奇点不变量以及大 Cohen-Macaulay 代数。最近的发现涉及有限性、米尔诺纤维的上同调、同调猜想和双有理几何。这次会议将利用这些新发展并将其灌输给当代研究生。更多信息可以在会议网站上找到：http://www-users.math.umn.edu/~cberkesc/localCohomConf2017