The principal investigator will direct the establishment of a "Regional Geometry Institute." Research mathematicians, graduate students, pre-college teachers, and high school students will form a community with the goal of learning dynamics while coming to understand each individual's special viewpoint. For the most part, this award will support the "Advanced Research Component," which over the course of the project will convene the foremost dynamical systems theorists in the world, college research faculty, and graduate students. Research activities in complex analytic dynamics, computational complexity, attractors, renormalization, annular maps, neural networks, and fractal geometry will be organized by several experts. Activities are also planned between summers. Coupled to this award will be a four-year project funded through the Division for Teacher Preparation and Enhancement (TPE-8954797). Entitled, "Contemporary Mathematics and Technology as a Driving Force for School Reform," this project will draw pre-college teachers from two Boston area school districts to the same environment to learn dynamics and methods by which these topics can be infused into the high school curriculum. Also coupled to these projects in the first year is a Young Scholars Project (RCD-8855151) entitled Project PROMYS- Program in Mathematics for Young Scientists. This ongoing project draws bright high school students together to study a variety of research problems in dynamical systems which have been tailored to their level of mathematics expertise. Participants from each of the three funded projects will have extensive opportunities to work together and learn from one another. Mixed groups will be formed for day-to-day discussions and field trips. These will study dynamics problems from several viewpoints. A well-equipped "Dynamics Lab" will be made available to all participants and is seen as a focal point for interaction activities.
