EMSW21-RTG Research Training in Geometry and Topology at Michigan State University

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AbstractAward: DMS-0353717Principal Investigators: Ronald A. Fintushel, Efstratia Kalfagianni,Thomas H. Parker, Jon G. wolfsonThe goal of this proposal is the enhancement of the researchtraining environment in geometry and topology at Michigan StateUniversity. Our goal is to use increased resources to improve:1. Recruitment at all levels --- undergraduate, graduate, andpostdoctoral.2. Graduate training, especially in terms of the diversity ofseminars, course offerings, and reducing the time to obtain aPh.D.3. The experience of postdoctoral fellows and their preparationfor a tenure-track position.4. Undergraduate participation with the Geometry/Topologyresearch group.5. Interaction among students and faculty at all levels.6. The research environment at all levels with a regular programof seminars and visiting mathematicians.The graduate students and postdoctoral assistants who will bementored under this proposal will contribute to research on ourmain focus, low-dimensional manifolds, using a wide variety oftechniques including gauge theory, geometric analysis,pseudoholomorphic maps, knot invariants, surgery techniques, andmapping class groups. Faculty at Michigan State University aswell as former students and postdoctoral assistants have takenpart in important advances in this rapidly progressing area, andit is expected that future students and postdoctoral fellows willcontinue in this direction.To further stimulate research, the MSU Geometry/Topology Groupwill initiate new programs for undergraduate and graduatestudents and postdoctoral fellows. The key to these seminars isthe atmosphere of collaborative learning that has been fosteredby the Geometry/Topology Group over the last fifteen years. Thebroader impact of this proposal will address the production ofresearch mathematicians and teachers of mathematics who areinterested in geometry and topology. The aim is to create anenvironment which encourages all involved to become betterteachers, better expositors, and better researchers, andencourages those entering mathematics to stay in the field.