Mathematical Sciences: Topology, Geometry, and Dynamics of Foliations

康伦将研究余维1的结构 叶理 纽结补集的叶理的存在， 叶状双曲结构，叶理的光滑性，以及 将研究遍历特性。这项工作扩展了 首席研究员的层次理论， 对叶理理论的发展产生了深远的影响， 与法国和日本的叶理学校的互动。 叶理的数学理论涉及充填 由表面或“叶子”堆叠而成的空间。 康伦帮助 证明任何表面都可以是叶理的叶子。 由于一些 表面包裹在自己身上，这个证明是非常困难的。 现在康伦将通过理解叶理来进一步发展他的理论 除了一个结之外，它填满了所有的空间。 的理解 最近对于理解 热力学和分子生物学。

Conlon will investigate the structure of codimension one foliations. The existence of foliations of knot complements, leafwise hyperbolic structures, smoothability of foliations, and ergodic properties will be studied. This work expands the Principal Investigator's theory of levels which has made a profound impact on development of foliation theory and has led to interaction with the French and Japanese schools of foliations. The mathematical theory of foliations concerns the filling of space by stacks of surfaces or "leaves". Conlon helped to prove that any surface may be a leaf of a foliation. Since some surfaces wrap upon themselves, this proof was very difficult. Now Conlon will further his theory by understanding foliations which fill all of a space except for a knot. The understanding of knots has recently become very important to the understanding of thermodynamics and molecular biology.