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

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AbstractAward: DMS 0739208Principal Investigator: Ronald A. Fintushel, EfstratiaKalfagianni, Thomas H. Parker, Jon G. WolfsonThe goal of this proposal is the enhancement of the researchtraining environment in geometry and topology at Michigan StateUniversity, building on our past success. The Geometry/TopologyGroup at MSU has a long-standing commitment to excellence ingraduate and postdoctoral training: we have produced someoutstanding graduate students, and we have been fortunate to haverecruited and mentored exceptional postdoctoral fellows. Ourgoal is to use increased resources to improve: (1) Recruitment atall levels --- undergraduate, graduate, and postdoctoral. (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 theirpreparation for a tenure-track position. (4) Undergraduateparticipation with the Geometry/Topology research group. (5)Interaction among students and faculty at all levels. (6) Theresearch environment at all levels with a regular program ofseminars and visitors.The graduate students and postdoctoral assistants who will bementored under this proposal will contribute to research ingeometry and topology, using a wide variety of techniquesincluding gauge theory, geometric analysis, pseudoholomorphicmaps, knot invariants, surgery techniques, 3-manifold topology,and mapping class groups. Faculty at Michigan State Universityas well as former students and postdoctoral assistants have takenpart in important advances in these rapidly progressing areas,and it is expected that future students and postdoctoral fellowswill continue in this direction. To further stimulate research,the MSU Geometry/Topology Group will initiate new programs andenhance existing programs for undergraduate and graduate studentsand postdoctoral fellows. The key to these programs is theatmosphere of collaborative learning that has been fostered bythe Geometry/Topology Group.This proposal will address the production of researchmathematicians and teachers of mathematics who are interested ingeometry and topology. This proposal will support 5 new graduatestudents and 2 new postdoctoral associates as well as one postdocand one graduate student who are being supported by our currentRTG grant. Our aim is to create an environment which encouragesall involved to become better teachers, better expositors, andbetter researchers, and encourages those entering mathematics tostay in the field.