Conference on Asymptotic and Effective Results in Complex Geometry

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DMS 0326849PI: S ZelditchJohns Hopkins UniversityConference on Asymptotic and Effective Results in Complex Geometry AbstractAbstract:This conference is devoted to asymptotic and effective results incomplex geometry. Many important problems in complex and algebraicgeometry concern the construction of holomorphic objects such asholomorphic sections of line bundles or maps between spaces. It oftenhappens that the construction problem simplifies as the degree of theline bundles or maps increases. A classical example is the Kodairaembedding theorem, which says that there are enough sections of a highpower of a positive line bundle to embed a Kahler manifold intoprojective space. Asymptotic results in general concern the propertiesof maps or sections of very high degree, where constructions oftensimplify. Effective results ask for the smallest power or degree where a desired effect takes place, e.g. the smallest power of a line bundle so that sections embed. Many such results will be surveyed in ourconference, with techniques ranging from partial differential equationsto geometric and algebraic methods.Our conference consists of seven days of lectures, with six to eightlectures a day. There will be lectures surveying past results and others which present new results. The topics include complexity ofzero-finding algorithms, moduli spaces, holomorphic maps, ground statesof superconductors, and the vacuum selection problem in string theory.The lectures will expose the field to graduate students, postdoctoralresearchers and junior faculty members, as well as to seniormathematicians. Two graduate students and at least five postdocs aregiving lectures. A significant portion of our funding will go towardspaying travel expenses of graduate students, young mathematicians andmembers of under-represented groups.