Mathematical Sciences: Investigations of Three-dimensional Manifolds and Their Mappings

McCullough将继续研究三维流形的结构和映射。在个人项目或与校外数学家的合作项目中，他将研究3流形的映射类群和微分同构群。技术将从几个领域，包括组合拓扑，双曲几何，和组合群论绘制。因为我们生活在三维宇宙中，所以理解三维流形是特别重要的对象。

McCullough will continue to work on structure and mappings of three-dimensional manifolds. In individual projects, or joint projects with off-campus mathematicians, he will work on the mapping class groups and diffeomorphism groups of 3-manifolds. Techniques will be drawn from several areas, including combinatorical topology, hyperbolic geometry, and combinatorial group theory. 3-manifolds are particularly important objects to understand, since we live in a 3-dimensional universe.