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

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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.