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

Michigan State University, East Lansing MI

Investigators

Abstract

Abstract Award: DMS-0353717 Principal Investigators: Ronald A. Fintushel, Efstratia Kalfagianni, Thomas H. Parker, Jon G. wolfson The goal of this proposal is the enhancement of the research training environment in geometry and topology at Michigan State University. Our goal is to use increased resources to improve: 1. Recruitment at all levels --- undergraduate, graduate, and postdoctoral. 2. Graduate training, especially in terms of the diversity of seminars, course offerings, and reducing the time to obtain a Ph.D. 3. The experience of postdoctoral fellows and their preparation for a tenure-track position. 4. Undergraduate participation with the Geometry/Topology research group. 5. Interaction among students and faculty at all levels. 6. The research environment at all levels with a regular program of seminars and visiting mathematicians. The graduate students and postdoctoral assistants who will be mentored under this proposal will contribute to research on our main focus, low-dimensional manifolds, using a wide variety of techniques including gauge theory, geometric analysis, pseudoholomorphic maps, knot invariants, surgery techniques, and mapping class groups. Faculty at Michigan State University as well as former students and postdoctoral assistants have taken part in important advances in this rapidly progressing area, and it is expected that future students and postdoctoral fellows will continue in this direction. To further stimulate research, the MSU Geometry/Topology Group will initiate new programs for undergraduate and graduate students and postdoctoral fellows. The key to these seminars is the atmosphere of collaborative learning that has been fostered by the Geometry/Topology Group over the last fifteen years. The broader impact of this proposal will address the production of research mathematicians and teachers of mathematics who are interested in geometry and topology. The aim is to create an environment which encourages all involved to become better teachers, better expositors, and better researchers, and encourages those entering mathematics to stay in the field.