EMSW21-RTG: Training the Research Workforce in Geometry, Topology and Dynamics

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AbstractAward: DMS-0602191Principal Investigator: Ralf Spatzier, Mario Bonk, Richard D. Canary, John E. Fornaess, Juha M. HeinonenThis proposal calls for a research training program in geometry,topology and dynamics at the University of Michigan. RecentPh.D.'s and advanced graduate students will be the mainbeneficiaries. The Mathematics Department at UM has one of thelargest and most vigorous post-doctoral and graduate programs inthe country with an excellent record of producing high-qualityresearchers in geometry, topology and dynamics. This proposalcalls to bolster the training of post-docs and graduate studentsin all of these areas by deepening and broadening it andproviding them with ample opportunities to excel in theirresearch. Five faculty members (Mario Bonk, Richard Canary, JohnErik Fornaess, Juha Heinonen and Ralf Spatzier) will lead thisproject in collaboration with eleven other senior faculty. Theproposal calls for several specific innovations in the trainingprogram by: providing intensive exploratory seminars andworkshops, travel semesters to deepen the scientific training atother insitutions at the forefront of research, opportunities todevelop lecturing skills, intensive mentoring and exposure toresearch in the three areas to undergraduates.Geometry, topology and dynamical systems are core areas ofmathematics. Geometry investigates the shape of spaces, throughinvariants such as curvature. Topology explores the propertiesof spaces which remain invariant under deformations such as thenumber of holes in a surface. Dynamical systems concern theevolution of a physical or mathematical system over time.Especially in recent years, they have developed in mutuallybeneficial interaction. Case in point are topology, geometry andcomplex dynamics in low dimension which in many aspects mirroreach other. Many of the most exciting developments in theseareas are truly interrelated, and benefit from each other eitherby idea, analogy or actual tool. At the same time, connectionswith other fields such as algebraic geometry and mathematicalphysics have strengthened dramatically. These developments havebeen amazing in their breadth and depth, and demonstrate thevitality of these areas. This project will train youngresearchers in these exciting and interconnected fields, and willhelp insure their future health and continued interaction.