Cohomology, curvature, classifying spaces and symmetry

利里教授将继续单独和合作研究几何群论和几何拓扑学。特别地，他将构造具有强不动点性质的无限群。这有望应用于Kropholler群体层次结构的研究。他还将研究他开发的保持同调的函子(从单纯复形到局部CAT(0)立方复形)。这项工作对拓扑学、K理论和群论都有一定的应用价值。他还将对所有以某种方式粘合多边形而成的具有最大可能对称群的空间进行分类。群是数学家对对称性概念的抽象：群测量对称性的方式与数字测量数量的方式相同。群论和几何学之间存在着令人着迷的联系。利里教授的目标是构造具有令人惊讶的性质组合的群，这应该会在几何学和群论中产生新的结果和见解。他还将对一族几何物体进行分类，这些物体概括了柏拉图式的固体，即至少已研究了4000年的五种对称形状。

Professor Leary will continue research on geometric group theory, and geometric topology, both alone and in collaboration. In particular, he will construct infinite groups having strong fixed point properties. This is expected to have application to the study of Kropholler's hierarchy of groups. He will also study a functor that he has developed (from simplicial complexes to locally CAT(0) cubicalcomplexes) that preserves homology. This work should have applications to topology, K-theory and group theory. He will also classify all spaces that can be built by gluing polygons in a certain way that have the `largest possible' groups of symmetries.A group is the mathematician's abstraction of the notion of symmetry:groups measure symmetry in the same way that numbers measure quantity.There are fascinating connections between group theory and geometry.Professor Leary aims to construct groups with surprising combinations of properties, which should lead to new results and insights within both geometry and group theory. He will also classify a family of geometrical objects which generalize the platonic solids, five symmetrical shapes that have been studied for at least four thousand years.