Frobenius Splitting in Algebraic Geometry, Commutative Algebra, and Representation Theory

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The property of a variety or ring being F-split (under mild conditions, equivalently F-pure) is an extremely powerful condition. Perhaps most famously, in the 1980s, these techniques were applied in the study of Schubert varieties, and continue to be actively used in the study of algebraic groups. On the other hand, in the 1970s, these techniques were used to prove fundamental results about rings of invariants by reductive groups. These methods anticipated the fundamental ideas behind the tight closure theory. In the 1990s, it was discovered that there is a precise dictionary between some of the notions coming from the minimal model program, and invariants defined by variants of Frobenius splitting and tight closure theory (a correspondence that is still not fully understood). Some of these methods are also related to the study of vector bundles in characteristic p, another active area of research which has had numerous applications.This conference that will take place at the University of Michigan, Ann Arbor, May 17th--May 22nd, 2010. The organizing committee consists of:M. Blickle (Universitat Duisburg-Essen), M. Brion (Universite de Grenoble), F. Enescu (Georgia State University), S. Kumar (University of North Carolina at Chapel Hill), M. Mustata (University of Michigan), K.Schwede (University of Michigan). The conference will focus on Frobenius splitting and related notions, methods, and applications to the following important areas of mathematics: the representation theory of algebraic groups, commutative algebra, and higher dimensional algebraic geometry. The conference will bring researchers together and stimulate communication between the various groups (communication which previously has been somewhat limited). It is expected that this conference will impact the mathematical community in a number of ways. Firstly, by exposing researchers to new potential applications of their own work and also to different points of view, the meeting will inspire new communication, collaboration and research. The participants of the conference will have different backgrounds, and thus many of the talks will necessarily be focused at a non-expert audience. Therefore, secondly, the talks given will be suitable for young mathematicians, especially graduate students and junior faculty. Finally, we also expect to attract other established researchers interested in learning about these techniques.