This award continues the partial (but essential) support of NSF for the fall meetings of the Workshop in Dynamical Systems and Related Topics for the years 2006, 2007, and 2008. This represents the Penn State half of the Semi-annual Workshop in Dynamical Systems and Related Topics, cosponsored for the last 15 years by the dynamics groups of Penn State and Maryland; the Maryland half is held each spring. The conference covers essentially all topics in dynamical systems, with a particular (but not exclusive) area of emphasis in most meetings. In the years 2006, 2007, and 2008 a Geometry session will be added to address growing activity in the borderline between dynamics and geometry. The goals of the conference are to promote the communication of mathematical results; to facilitate interaction and progress in dynamical systems and related fields; to nurture the sense of community and common mission in these fields; and to contribute to the training of graduate students and recent Ph.D. recipients and to their integration into the dynamics community. In particular, the conference includes special sessions with about 8 short talks by graduate students who received some interesting new results. Over the years the conference has enjoyed the participation of many prominent mathematicians, as well as (we see now) future leaders. A history of past programs can be found at www.math.psu.edu/research/dynsust/dw.html and www.math.psu.edu/research/dynsust/dw-archive.html.
In general terms, the field of dynamical systems studies the way in which systems change over time, especially, how typical trajectories of a system behave over time, and when properties of interest in a system are stable under perturbations of the system. Because so many mathematical structures can be considered in terms of how they change over time, dynamical systems uses a broad range of mathematical disciplines (including differential equations, functional analysis, geometry, probability theory and many others). Conversely, the dynamical approach has contributed significantly to progress in some of these fields, at a deep and nonobvious level. A recent example -- in number theory! is the dynamical influence on the work of Green and Tao which showed that the prime numbers contain arbitrarily long arithmetic progressions. In addition, various practical problems are fruitfully studied from the viewpoint of dynamical systems, including current applications in weather forecasting and the computation of orbits of space "voyagers". Another example is study of "chaos": modern methods of rigorous mathematical description of "chaos" are based on Pesin's Theory developed by Ya. Pesin, a member of the Penn State Center for Dynamics and Geometry and on pioneering works of J. Yorke, a member of the Maryland dynamics group.
