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次关于有限陈述的可解决群体的会议。在1983年国际数学家大会上的演讲中，格罗莫夫谈到群是几何对象。这是他在1981年证明多项式增长的有限生成群包含有限指数的幂零子群的结果，这有助于将注意力集中在有限生成可解群的渐近性质对其代数结构的影响程度上。这导致了一些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产生的思想所推动的，其中半单群表现出可解群所不具有的刚性。这种正在进行的几何研究可能是最简单的有限生成可解群，它突出了有限表示可解群的本质。小组出现在数学、物理、化学和晶体学等学科的许多不同领域。其中一个原因是它们可以被用作理解和定义对称性的工具。许多教堂的地板图案表现出一种对称性，可以用群论来分析和更好地理解，正是这种对称性被团体捕捉到，但以一种更抽象的方式。群本身也显示出一种与生俱来的对称性，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。这次会议的目的是将现有的群论的组合和理论方法与几何方法结合起来。后者需要大量的数学机器。目前正在进行的工作涉及由Evarste Galois(他于1832年死于一场决斗，年仅21岁)引入的可解群，以确定日常多项式方程的解的性质。会议的目的是向研究生、博士后和感兴趣的专业人士提供群论的这两个方面。

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.