Finitely presented solvable groups at The City College of New York, Fall 2010 conference

这个项目是为了支持2010年秋季在纽约城市学院举行的一个关于可解群的会议。格罗莫夫在1983年国际数学家大会上的演讲中谈到了几何对象的群体。这是继他的证明在1981年，即生成群的多项式增长包含一个幂零子群的有限指数，这有助于集中注意力的程度上的渐近性质的一个生成群的可解的代数结构。这导致了许多关于可解群的拟等距和刚性的结果，其中一些结果是由李群理论中的思想所激发的，其中半单群表现出的刚性是可解群所不具有的。这是正在进行的几何研究什么也许是最简单的可解群生成的可解群已经把尖锐的救济非常性质的可解群。群体出现在数学、物理、化学和其他学科中的许多不同领域。其中一个原因是它们可以作为理解和定义对称性的工具。许多教堂的地板图案显示出一种对称性，可以通过使用群论来分析和更好地理解，而群论所捕捉的正是这种对称性，但以一种更抽象的方式。群也显示出它们自身固有的对称性，近年来人们努力将几何学与群论联系起来。这是当前研究的一个重要领域。本次会议的目的是加入现有的组合和理论方法的群论的几何方法。后者需要大量的数学机器。 目前正在进行的工作涉及可解群介绍了埃瓦里斯特伽罗瓦（谁死于1832年在决斗年龄21），以确定性质的解决方案的日常多项式方程。会议的目的是使群论的两个方面提供给研究生，博士后和感兴趣的专业人士。

This project is to support a conference on Finitely presented solvable groups at The City College of New York, Fall 2010. In his address to the International Congress of Mathematicians in 1983, Gromov talked about groups as geometric objects. This followed on his proof in 1981 that finitely generated groups of polynomial growth contain a nilpotent subgroup of finite index, which has helped to focus attention on the extent to which the asymptotic properties of a finitely generated solvable group has on its algebraic structure. This has led to a number of results dealing with the quasi-isometries and rigidity of solvable groups.Some of these results have been motivated by ideas coming out of the theory of lie groups, where the semi-simple ones exhibit a rigidity that is not shared by the solvable ones. This ongoing geometric study of what are perhaps the simplest finitely generated solvable groups has put into sharp relief the very nature of finitely presented solvable groups. Groups arise in many different areas of mathematics, in physics, in chemistry and in chrystallography among other disciplines. One of the reasons for this is that they can be used as a tool for understanding and defining symmetry. Floor patterns in many churches display a symmetry which can be analyzed and better understood by using group theory and it is this kind of symmetry that groups capture, but in a more abstract way. Groups also display an innate symmetry of their own and in recent years efforts have been made to connect geometry to group theory. This is an important area of current research. The objective of this conference is to join the existing combinatorial and theoretical approach of group theory to the geometric approach. The latter requires a great deal of mathematical machinery. The work that is currently being undertaken involves solvable groups introduced by Evariste Galois (who died in 1832 in a duel aged 21) to determine the nature of the solutions of everyday polynomial equations. The aim of the conference is to make the two aspects of group theory available to graduate students, postdocs and interested professionals.