PASI: Commutative Algebra and its Connections to Geometry; Olinda, Brazil, Summer 2009

这项由美国国家科学基金会（NSF）和美国能源部（DOE）联合支持的泛美高级研究所（PASI）奖将于2009年夏天在巴西奥林达的伯南布哥联邦大学举行。由普渡大学的Bernd Ulrich组织，PASI将讨论交换代数的最新发展及其与几何的联系。这些活动将集中在以下几组现代交换代数的核心主题：同调猜想、正和混合特征的问题、紧闭及其与双对数几何的相互作用、积分依赖和爆破代数、组合交换代数、Gröbner基和计算代数等。该活动将促进主要来自西半球的代数学家和几何学家之间的协作互动。该项目将汇集理想的参与者组合，从研究生到博士后，再到初级和高级教师。这次PASI的预期结果将包括：有机会在他们职业生涯的不同阶段和具有不同数学品味和背景的研究人员之间建立牢固和持久的联系。招聘将通过为PASI开发的网站、专业协会的通讯和电子邮件列表进行。PASI的结果将通过PASI网站和学校的一卷会议记录进行传播，作为未来活动的参考。

This Pan-American Advanced Studies Institutes (PASI) award, jointly supported by the NSF and the Department of Energy (DOE), will take place during the summer of 2009 at the Universidade Federal de Pernambuco in Olinda, Brazil. Organized by Bernd Ulrich of Purdue University, the PASI will address recent developments in commutative algebra and their connections to geometry. The activities will focus on the following clusters of topics central to modern commutative algebra: the homological conjectures, problems in positive and mixed characteristic, tight closure and its interaction with birational geometry, integral dependence and blowup algebras, combinatorial commutative algebra, Gröbner bases, and computational algebra, among others.The activity will promote collaborative interactions among algebraists and geometers mostly of the Western Hemisphere. The program will bring together an ideal mix of participants from graduate students to post-docs to junior and senior faculty. Expected outcomes in this PASI will include: the opportunity to forge strong and lasting ties among researchers at different stages of their careers and with diverse mathematical tastes and backgrounds. Recruitment will be done through a web-site developed for the PASI, newsletters of professional societies, and e-mail lists. Results from the PASI will be disseminated through the PASI website and a volume of proceedings of the school as a reference on which to build future activities.