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Noncommutative differential geometry is a novel approach to geometry that is paving the way for exciting new directions in the development of mathematics and physics. The contributions in this volume are based on papers presented at a workshop dedicated to enhancing international cooperation between mathematicians and physicists in various aspects of frontier research on noncommutative differential geometry. The active contributors present both the latest results and comprehensive reviews of topics in the area. The book is accessible to researchers and graduate students interested in a variety

Mathematical physics --- Noncommutative differential geometry --- Differential geometry, Noncommutative --- Geometry, Noncommutative differential --- Non-commutative differential geometry --- Infinite-dimensional manifolds --- Operator algebras

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The Romanian conferences in operator theory, as they are now commonly called, havestartedintheyear1976asanannualworkshoponoperatortheoryheldatthe University of Timi¸ soara, originally only with Romanian attendance. The meeting soon evolved into an international conference, with an increasingly larger parti- pation. It has been organized jointly, initially by the Department of Mathematics of INCREST and by the Faculty of Sciences of the University of Timi¸ soara, then (since 1990) by the Institute of Mathematics of the Romanian Academy and the Faculty of Mathematics of the West University of Timi¸ soara. The venue was u- ally Timi¸ soara (and, occasionally, Herculane, Bucharest or Predeal). Since 1986 the conference has been regularly held biannually at the beginning of the summer. The 19th Conference on Operator Theory (OT 19) took place between June 27th and July 2nd 2002, at the West University of Timi¸ soara. It is a pleasure to acknowledge the considerable ?nancial support received through the p- gramme EURROMMAT of the European Community, under contract ICA1-CT- 2000-70022. Partial support has also been provided by the Romanian Ministry of Education, Research and Youth, grants CERES 152/2001 and 153/2001. The full programme of the conference is included in the sequel. It is worth mentioning also a special event that has taken place during the conference: p- fessor Israel Gohberg has been awarded the title of Doctor Honoris Causa of the West University of Timi¸ soara.

Operator theory --- Operator algebras --- Functional analysis. --- Global analysis (Mathematics). --- Operator theory. --- Topological Groups. --- Integral equations. --- Distribution (Probability theory. --- Functional Analysis. --- Analysis. --- Operator Theory. --- Topological Groups, Lie Groups. --- Integral Equations. --- Probability Theory and Stochastic Processes. --- Equations, Integral --- Functional equations --- Functional analysis --- Groups, Topological --- Continuous groups --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Functional calculus --- Calculus of variations --- Integral equations --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematical analysis. --- Analysis (Mathematics). --- Topological groups. --- Lie groups. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- 517.1 Mathematical analysis --- Mathematical analysis