Mathematical Sciences: Knotting and Linking Phenomena in Topology

点击翻译按钮获取中文摘要

9400224 Cochran Dr. Cochran will study invariants which characterize links and graphs in n-dimensional space, particularly in 3-dimensional space. More broadly, he will study the classification of 3-dimensional manifolds with large fundamental group, modulo homology cobordism, and the related problems of topological surgery on 4-dimensional manifolds and the classification of 4-dimensional manifolds. Dr. Cochran will study properties of shape associated to configurations of circles and to graphs in three-dimensional space (knot theory). These studies of properties of shape are important in many ways. For example, one primary strategy for the development of new anti-viral drugs is as follows. First, understand the topology or shape of the virus. Second, find a protein with a "complementary" topology or shape which can thus be used to "plug up" the active sites on the virus. Unfortunately, the vast numbers of possible proteins assume largely unknown and complex, twisted and knotted shapes in 3-dimensional space. Therefore studies of properties of shape are needed to assist this endeavour. Dr. Cochran will be in contact with scientists from the Keck Institute for Computational Biology at Rice University. ***