Mathematical Sciences: Algebraic Problems Arising Out of Cohomology of Groups, Fixed point Theory and Shape

纪勤教授的兴趣领域是拓扑学和相关群论。他将研究几何和同调群理论中的问题，这些问题的拓扑方法来自形状理论、不动点理论和无限维拓扑。更具体地说，他将研究涉及群的有限性质和上同调性质的各种问题，这些问题可以解释为关于覆盖空间的“目的”的问题。他将继续与康奈尔大学的K.S.布朗教授在无限维有限呈现离散群方面的合作。他将独自继续研究H.Bass关于具有群环的幂等矩阵的Hattori-Stallings迹的一个著名猜想的拓扑意义。群在数学和自然科学中作为对称性的编码符号无处不在，人们用再多的方法也不会有太多的方法来发现它们的性质。

Professor Geoghegan's areas of interest are topology and related group theory. He will investigate problems in geometric and homological group theory for which topological methods, coming from shape theory, fixed point theory and infinite- dimensional topology, are appropriate. More specifically he will investigate various questions involving finiteness properties and cohomological properties of groups which can be interpreted as questions about "ends" of covering spaces. He will continue his collaboration with Professor K.S. Brown of Cornell University on infinite-dimensional finitely presented discrete groups. On his own he will continue his investigation of the topological meaning of a well known conjecture of H. Bass about the Hattori-Stallings trace of an idempotent matrix with group ring entries. Groups are ubiquitous in mathematics and the natural sciences as codifiers of symmetry, and one can never have too many approaches to discovering their properties.