Conference on Asymptotic and Effective Results in Complex Geometry

复杂几何渐近有效结果会议

• 批准号: 0326849
• 负责人: Steve Zelditch
• 金额: $ 2.1万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-05-01 至 2005-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0326849&HistoricalAwards=false
• 关键词: Conference; Asymptotic; Effective; Results; Complex

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.

DMS 0326849 PI：S Zelditch约翰霍普金斯大学复几何中的渐近和有效结果会议 摘要：本次会议致力于复几何中的渐近和有效结果。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。 当线丛或映射的次数增加时，构造问题往往变得简单。 一个经典的例子是Kodaira嵌入定理，它说有足够的部分的高功率的正的线丛嵌入一个卡勒流形到射影空间。渐近结果一般涉及非常高次的映射或截面的性质，其中的构造常常是简化的。有效的结果要求最小的功率或程度，其中所需的效果发生，例如，最小功率的线束，使部分嵌入。 许多这样的结果将在我们的会议中进行调查，技术范围从偏微分方程到几何和代数方法。我们的会议包括七天的讲座，每天六到八个讲座。将有讲座调查过去的结果和其他提出新的结果。 课程的主题包括零发现算法的复杂性，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，博士后研究人员和初级教师以及高级数学家展示该领域。 两名研究生和至少五名博士后正在讲课。 我们很大一部分资金将用于支付研究生、年轻数学家和代表性不足群体成员的差旅费。