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

Michigan State University, East Lansing MI

Investigators

Abstract

Abstract Award: DMS 0739208 Principal Investigator: 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, building on our past success. The Geometry/Topology Group at MSU has a long-standing commitment to excellence in graduate and postdoctoral training: we have produced some outstanding graduate students, and we have been fortunate to have recruited and mentored exceptional postdoctoral fellows. 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 visitors. The graduate students and postdoctoral assistants who will be mentored under this proposal will contribute to research in geometry and topology, using a wide variety of techniques including gauge theory, geometric analysis, pseudoholomorphic maps, knot invariants, surgery techniques, 3-manifold topology, and mapping class groups. Faculty at Michigan State University as well as former students and postdoctoral assistants have taken part in important advances in these rapidly progressing areas, 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 and enhance existing programs for undergraduate and graduate students and postdoctoral fellows. The key to these programs is the atmosphere of collaborative learning that has been fostered by the Geometry/Topology Group. This proposal will address the production of research mathematicians and teachers of mathematics who are interested in geometry and topology. This proposal will support 5 new graduate students and 2 new postdoctoral associates as well as one postdoc and one graduate student who are being supported by our current RTG grant. Our 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.