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

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

Abstract Award: DMS-0602191 Principal Investigator: Ralf Spatzier, Mario Bonk, Richard D. Canary, John E. Fornaess, Juha M. Heinonen This proposal calls for a research training program in geometry, topology and dynamics at the University of Michigan. Recent Ph.D.'s and advanced graduate students will be the main beneficiaries. The Mathematics Department at UM has one of the largest and most vigorous post-doctoral and graduate programs in the country with an excellent record of producing high-quality researchers in geometry, topology and dynamics. This proposal calls to bolster the training of post-docs and graduate students in all of these areas by deepening and broadening it and providing them with ample opportunities to excel in their research. Five faculty members (Mario Bonk, Richard Canary, John Erik Fornaess, Juha Heinonen and Ralf Spatzier) will lead this project in collaboration with eleven other senior faculty. The proposal calls for several specific innovations in the training program by: providing intensive exploratory seminars and workshops, travel semesters to deepen the scientific training at other insitutions at the forefront of research, opportunities to develop lecturing skills, intensive mentoring and exposure to research in the three areas to undergraduates. Geometry, topology and dynamical systems are core areas of mathematics. Geometry investigates the shape of spaces, through invariants such as curvature. Topology explores the properties of spaces which remain invariant under deformations such as the number of holes in a surface. Dynamical systems concern the evolution of a physical or mathematical system over time. Especially in recent years, they have developed in mutually beneficial interaction. Case in point are topology, geometry and complex dynamics in low dimension which in many aspects mirror each other. Many of the most exciting developments in these areas are truly interrelated, and benefit from each other either by idea, analogy or actual tool. At the same time, connections with other fields such as algebraic geometry and mathematical physics have strengthened dramatically. These developments have been amazing in their breadth and depth, and demonstrate the vitality of these areas. This project will train young researchers in these exciting and interconnected fields, and will help insure their future health and continued interaction.