A Center of Excellence in the Mathematical Sciences - at Cornell University
Final rept. 1 Jan 1986-31 Jan 1992
CORNELL UNIV ITHACA NY
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Significant discoveries were made concerning the role of symmetry in dynamical systems, work on the dynamics of low-dimensional dynamical systems one and two dimensional real and complex systems, and progress in the use of symbolic computation tools for the study of dynamical systems. The development of the visualization tool and interface for studying dynamical systems, kaos, was partially funded through MSI. Research in interacting particle systems increased as they are attractive models useful in a wide variety of situations in physics, biology, and image processing. One of the great breakthroughs in the subject in the past five years was R. Durretts development of methods for treating large classes of these models if one is willing to assume that the range of interaction is large or that the particles are moving at a fast rate. These assumptions are satisfied in many biological and physical systems and provide a reliable guide to the qualitative features of other systems, as well. Very significant work was done in the area of polytopes, generalized discriminants, and resultants. They established a conjecture of Baues arising in the geometry of loop spaces in homotopy theory. Research and development was done on Macaulay which has become one of the major computer algebra systems for computations in algebraic geometry and commutative algebra. The system is in use world-wide. MSI-funded research ranged from the development of new, underlying theoretical mathematics to the actual implementation of the program. Automatic techniques were developed to generate differential equations that model physical systems. The work uses symbolic computation to generate the equations and ties together symbolic and numerical methods to make the equations easier to solve.
- Particle Accelerators