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

该项目是为了支持2010年秋季在纽约城市学院举行的有限呈现可解群会议。在1983年国际数学家大会的演讲中，格罗莫夫谈到了群作为几何对象。他在1981年证明了多项式增长的有限生成群包含有限指数的幂零子群，这有助于关注有限生成可解群的渐近性质对其代数结构的影响程度。这导致了一些处理准等距和刚性的可解群的结果。其中一些结果是由李群理论的观点所激发的，在李群理论中，半简单群表现出一种刚性，而可解群却没有这种刚性。这种正在进行的关于可能是最简单的有限生成可解群的几何研究，使有限呈现的可解群的本质得到了鲜明的体现。在数学、物理、化学、结晶学和其他学科的许多不同领域都出现了小组。其中一个原因是，它们可以作为理解和定义对称的工具。许多教堂的地板图案显示出一种对称性，这种对称性可以用群论来分析和更好地理解，而群体正是以一种更抽象的方式捕捉到了这种对称性。群体本身也表现出一种天生的对称性，近年来，人们努力将几何与群论联系起来。这是当前研究的一个重要领域。本次会议的目的是将现有的群论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Evariste Galois（他于1832年死于一场决斗，享年21岁）引入的可解群，以确定日常多项式方程解的性质。这次会议的目的是让研究生、博士后和感兴趣的专业人士了解群论的两个方面。

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.