Commutative Algebra and Its Interactions with Algebraic Geometry

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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.