EMSW21-RTG-Program in low-dimensional topology and its applications

项目负责人：Alan W. Reid, Robert E. Gompf,Cameron M. Gordon, John E. luecke。该RTG方案主要研究低维拓扑训练及其应用。低维流形的研究已成为数学研究的中心领域之一。PI在低维拓扑的几个不同领域都有研究成就的记录；例如，结理论，3流形和4流形拓扑，双曲流形和辛拓扑。该项目还将允许PI继续培养博士后和学生。这个RTGProposal的主题与数学的其他几个分支以及应用科学相互作用。因此，它为各级的研究、教育和培训经验提供了肥沃的土壤。该建议的主要特点之一是建立和提升目前数学系成功的培训和教育结构。然而，我们提议的一个重要的新组成部分是跨学科研究的培训。这将为博士后、研究生和本科生提供不同于传统的教育和培训体验。因此，我们的目标是提供一个支持传统意义上的教学和培训的框架，并为拓扑在物理和生物科学中的应用提供培训经验的机会。作为后一项努力的一部分，该项目将促进与研究DNA打结现象和生物医学数学的科学家的互动。作为我们推广工作的一部分，我们将发起一个公共系列讲座，以提高拓扑学在大学和当地社区其他科学中的作用的形象和意识水平。

AbstractAward: DMS-0636643Principal Investigator: Alan W. Reid, Robert E. Gompf,Cameron M. Gordon, John E. LueckeThis RTG proposal is focused on training in low-dimensionaltopology and its applications. The study of low-dimensionalmanifolds has become one of the central areas of researchactivity in mathematics. The PI's have an establishedtrack-record of research accomplishments in several differentareas of low-dimensional topology; for example knot theory, 3 and4-manifold topology, hyperbolic manifolds and symplectictopology. The project will also allow the PI's to continue theirtraining of postdocs and students. The subject of this RTGProposal interacts with several other branches of mathematics aswell as the applied sciences. It therefore provides fertileground for research, education and training experiences at alllevels.One of the main features of the proposal is to build, andelevate, the successful structure for training and educationcurrently in place in the Department of Mathematics. However, animportant new component of our proposal is training forinterdisciplinary research. This will afford postdocs, graduateand undergraduate students educational and training experiencesdifferent from the traditional ones available at present. Wetherefore aim to provide a framework that supports education andtraining by instruction in the traditional sense, and alsoprovide opportunity for training experiences in applications oftopology in the physical and biological sciences. As part of thislatter effort the project will promote interactions withscientists studying knotting phenomena in DNA and biomedicalmathematics. As part of our outreach efforts, we will instigatea public lecture series that will raise the profile and level ofawareness of the role of topology in other sciences in theUniversity and local community.