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

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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.