International travel support for US researchers to attend '60 Miles,' London, July 2008

“60英里”会议以不同寻常的密度和广度汇集了最高水准的演讲者。它可以说是2008年的终极代数几何事件。Miles Reid是从20世纪80年代开始并持续至今的革命性的最小模型计划（MMP）的主要原始建筑师之一。这次会议是为了庆祝他的60岁生日，但除此之外，也许更重要的是，它汇集了高维代数几何中最好的。这次会议与该领域一位领导者的生日有关，这一事实保证了演讲者和参与者的名单确实很壮观。MMP是作为代数变量（由代数方程定义的几何对象）分类的工具而开发的。黎曼和他同时代的人已经知道曲线理论，而意大利古典学派已经知道曲面理论。表面理论是由Kodaira在20世纪60年代完成的。由于20世纪70年代发现的结果，人们认为在高于2维的维度上不可能有类似的理论。Miles Reid的工作改变了这一观点，并导致Reid和Mori以及Kawamata、Kollar和Shokurov取得了突破性的结果。由于他对该理论的贡献，森在1990年获得了菲尔兹奖，这反映了该理论在代数几何中的重要性。MMP在20世纪80年代完成了3倍折叠，当时大部分都是在任意维度上开发的，留下了一个中心问题，这个问题持续了四分之一个世纪。最近，Hacon和McKernan在这个尚未解决的问题上取得了非凡的突破，这引起了轰动，并重新点燃了人们对该理论发展的兴趣（对其应用的兴趣从未消退）。会议邀请了12位世界知名的演讲者，其中包括大多数MMP的主要人物，2位领域奖章获得者，至少9位ICM演讲者。目前资助的主要目的是使初级研究人员，包括一些研究生有可能参与这一独特的活动。

ABSTRACTThe conference 60 Miles brings together the highest caliber speakers in an unusual density and broadness. It is arguably the ultimate algebraic geometry event of 2008.Miles Reid has been one of the main original architects of the revolutionary Minimal Model Program (MMP) starting in the 1980s and continuing today. This conference celebrates his 60th birthday, but beyond that occasion, perhaps more importantly, it brings together the best of the best in higher dimensional algebraic geometry. The fact that this conference is related to the birthday of one of the leaders of the field is assurance that the list of speakers and participants is truly spectacular.The MMP was developed as a tool in the classification of algebraic varieties (geometric objects defined by algebraic equations). The theory for curves was already known to Riemann and his contemporaries and for surfaces the classical Italian school. The surface theory was completed by Kodaira in the 1960s. Due to results discovered in the 1970s, it was believed that a similar theory was not possible in dimensions higher than two. That view was altered by the work of Miles Reid and lead to groundbreaking results by Reid and Mori as well as by Kawamata, Kollar and Shokurov. For his contribution to the theory, Mori received the Fields Medal in 1990 reflecting on the importance the theory plays in algebraic geometry.The MMP was completed for 3-folds in the 1980s and most of it was developed in arbitrary dimension at that time, leaving one central problem open for a quarter of a century. Recently Hacon and McKernan achieved an extraordinary breakthrough on that open problem which created a buzz and rekindled interest in the development of the theory (interest in its applicationa never faded).The conference features 12 world famous speakers including most of the major figures in MMP, 2 Field Medalists at least 9 ICM speakers. The present grant's main purpose is to make it possible for junior researchers, including some graduate students to participate in this unique event.