Conference on Asymptotic and Effective Results in Complex Geometry

S·泽尔迪奇约翰·霍普金斯大学关于复几何渐近和有效结果的会议摘要：这次会议致力于研究复几何的渐近和有效结果。复几何和代数几何中的许多重要问题都涉及到全纯对象的构造，如线丛的全纯截面或空间之间的映射。通常情况下，随着线束或地图的度数的增加，构造问题会简化。一个经典的例子是Kodaira嵌入定理，它说一个正线丛的高次方有足够的截面将Kahler流形嵌入到射影空间中。渐近结果一般涉及高次映射或高次截面的性质，其中构造往往是简化的。有效的结果要求在发生期望效果的地方功率最小或程度最小，例如，线束的最小功率，以便分段嵌入。我们的会议将用从偏微分方程组到几何和代数方法的技术来考察许多这样的结果。我们的会议由七天的讲座组成，每天有六到八节课。将有回顾过去成果的讲座和呈现新成果的其他讲座。课程主题包括求零算法的复杂性、模空间、全纯映射、超导体的基态，以及弦理论中的真空选择问题。讲座将向研究生、博士后研究人员、初级教员以及高级数学家介绍该领域。两名研究生和至少五名博士后正在讲课。我们的资金中有很大一部分将用于支付研究生、年轻数学家和代表性不足群体成员的旅费。

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.