Mathematical Sciences: Knotting and Linking Phenomena in Topology

9400224 Cochran Cochran博士将研究n维空间，特别是三维空间中的链接和图的不变量。更广泛地，他将研究具有大基群的三维流形的分类，模同调协，以及四维流形的拓扑手术和四维流形的分类的相关问题。科克伦博士将研究与三维空间中的圆和图形的构型相关的形状特性（结理论）。这些对形状特性的研究在很多方面都很重要。例如，开发新的抗病毒药物的一个主要策略如下。首先，了解病毒的拓扑结构或形状。其次，找到一种具有“互补”拓扑或形状的蛋白质，从而可以用来“堵塞”病毒上的活性位点。不幸的是，大量可能的蛋白质在三维空间中呈现出很大程度上未知的、复杂的、扭曲的和打结的形状。因此，需要对形状特性的研究来协助这一努力。科克伦博士将与莱斯大学凯克计算生物学研究所的科学家联系。＊＊＊

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. ***