Mathematical Sciences: The Norbert Wiener Centenary Congress;East Lansing, Michigan; November 27-December 3, 1994

9411399曼德雷卡大会的目标是追忆诺伯特·维纳的遗产，并记录其在正在进行的研究中的延续。这一遗产首先包括爱因斯坦的布朗运动理论的理想化。在此背景下，Wiener的工作构成了随机积分、随机微分方程和无限维空间上的积分的基础。概率论中的这三个主要领域在工程、控制理论、金融和量子物理中都有重要的应用。这项遗产还包括维纳在广义调和分析方面的工作，这项工作产生了许多影响，最新的是小波理论，这反过来又被用于数据存储的统计应用中。此外，Dirichlet问题的容量和广义解的概念也是遗留下来的，S在20世纪90年代得到了对p1阶非线性偏微分方程组的很好的推广。Norbert Wiener的概率论思想导致了位势理论和调和分析基本问题的求解。今天，这些领域正在积极推进，大会将努力激励年轻的概率学家和分析家以他的创新方式继续维纳的工作。

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.