Recent Developments in Higher Dimensional Algebraic Geometry Conference

高维代数几何会议的最新进展

• 批准号: 0515842
• 负责人: Vyacheslav Shokurov
• 金额: $ 1.7万
• 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: 2006
• 资助国家: 美国
• 起止时间: 2006-01-01 至 2006-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0515842&HistoricalAwards=false
• 关键词: Recent; Developments; Higher; Dimensional; Algebraic

The Johns Hopkins University Department of Mathematics, together with theJapan-U.S. Mathematics Institute (JAMI), will hold a conference andworkshop in March 2006 under the title "Recent developments in higherdimensional algebraic geometry". The main focus of the proposed activitywill be birational geometry. Finding good birational models of algebraicvarieties and understanding the way these appear is the main achievementof the minimal model program. The activity will cover related topics ofinterest: derived categories, Fano varieties, Mori-Fano fiber spaces,explicit 3-fold geometry, minimal log discrepancies, singularities,rational curves and connectivity. Geometry is one of the oldest mathematical subjects. The Greeks weredescribing geometrical objects using congruence (of segments, angles,...) and incidences (collinearity, tangency, ...). Congruence evolvedinto the modern-day differential geometry. Incidences evolved intoalgebraic geometry simply by replacing geometrical shapes by theequations defining them. The objects of study of algebraic geometry arecalled algebraic varieties. Understanding the structure of algebraicvarieties is of fundamental importance from both the standpoint ofalgebraic geometry alone, and from that of the related disciplines andareas of application - mathematical physics, computational geometry,number theory, and others. Knowledge of algebraic varieties is alsoimportant in applied fields, such as optimization, control, statistics,economics and bioinformatics, coding, complexity and communications.

约翰霍普金斯大学数学系与日美数学研究所将于2006年3月举行一次题为“高维代数几何的最新发展”的会议和讲习班。本次活动的重点是双有理几何。找到代数簇的好的双有理模型并理解它们出现的方式是最小模型程序的主要任务。活动将涵盖相关的主题ofinterest：派生类别，法诺品种，Mori-Fano纤维空间，明确的3倍几何，最小的日志差异，奇点，合理的曲线和连通性。几何学是最古老的数学学科之一。希腊人用（线段、角等）的全等来描述几何物体。和发生率（共线性、相切等）。同余演化成了现代的微分几何。事件演变成代数几何简单地取代几何形状的方程定义他们。代数几何的研究对象是代数簇.理解代数簇的结构，无论从代数几何本身的观点来看，还是从相关学科和应用领域（数学物理、计算几何、数论等）的观点来看，都具有根本的重要性。代数簇的知识在应用领域也很重要，如优化、控制、统计、经济和生物信息学、编码、复杂性和通信。