Recent Developments in Higher Dimensional Algebraic Geometry Conference

约翰霍普金斯大学数学系与日美数学研究所(JAMI)将于2006年3月举行一次题为“高维代数几何的最新发展”的会议和研讨会。拟议活动的主要焦点将是双曲面几何。找到好的代数变种的双态模型并理解它们的出现方式是最小模型程序的主要成果。本活动将涵盖感兴趣的相关主题：派生范畴、Fano簇、Mori-Fano纤维空间、显式三重几何、最小对数偏差、奇点、有理曲线和连通性。几何是最古老的数学学科之一。希腊人用(线段、角度等的)同余来描述几何物体。和偶然性(共线、相切等)。同余演化成了现代的微分几何。通过用定义几何形状的方程来代替几何形状，关联就演变成了代数几何。代数几何的研究对象叫代数族。无论是从代数几何的角度，还是从数学物理、计算几何、数论等相关学科和应用领域的角度，理解代数族的结构都是非常重要的。在优化、控制、统计学、经济学和生物信息学、编码、复杂性和通信等应用领域，代数变体的知识也很重要。

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.