9411399 Mandrekar The objective of the Congress is to recall the legacy of Norbert Wiener and record its continuation in ongoing research. The legacy comprises first the idealization of Einstein's theory of Brownian motion. Wiener's work in this context constitutes the foundation of the stochastic integration, stochastic differential equations, and integration on infinite-dimensional spaces.. These three major fields in probability have significant applications to engineering, control theory, finance, and quantum physics. The legacy also includes Wiener's work on generalized harmonic analysis, which has had numerous ramifications, the most recent being the theory of wavelets, which in turn is being used in the statistical application for the storage of data. In addition, the legacy comprises the notions of capacity and generalized solution of the Dirichlet problem, which in the 1990's has received a beautiful extension to nonlinear PDE's of order p > 1. Probabilistic ideas of Norbert Wiener have led to the solu ions of fundamental problems of Potential Theory and Harmonic Analysis. These areas are being actively pursued today and the Congress will strive to inspire young probabilists and analysts to continue Wiener's work in his innovative way.
