Conference on Asymptotic and Effective Results in Complex Geometry

DMS 0326849PI: S ZelditchJohns Hopkins university of Complex Geometry in渐近有效结果会议摘要摘要：本次会议致力于讨论复杂几何的渐近有效结果。复杂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，如线束的非全纯截面或空间之间的映射。通常情况下，随着线束或地图的程度增加，构造问题会简化。一个经典的例子是kodaira嵌入定理，它说有足够多的高次正线束的部分可以将Kahler流形嵌入到射影空间中。渐近结果一般涉及到非常高次的映射或截面的性质，在这些性质中构造往往被简化。有效的结果要求最小的功率或程度，在期望的效果发生，例如，最小的功率线束，以使部分嵌入。许多这样的结果将在我们的会议上进行调查，技术范围从偏微分方程到几何和代数方法。我们的会议由七天的讲座组成，每天有六到八场讲座。将有讲座回顾过去的成果，也有讲座介绍新的成果。主题包括寻零算法的复杂性，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。这些讲座将向研究生、博士后研究人员、初级教员以及高级数学家展示这一领域。两名研究生和至少五名博士后正在授课。我们的很大一部分资金将用于支付研究生、年轻数学家和弱势群体成员的旅费。

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.