Fourteenth International Conference on Banach Algebras

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The Fourteenth International Conference on Banach Algebras willbe held at Pomona College in Claremont, California, from July 25through August 7, 1999. This series of conferences emphasizes bothBanach algebras and their connections with other areas of analysis.The title of this conference is "Banach Algebras and Operators onBanach Spaces". The formal conference program will involve aboutsixty talks on the general theory of Banach algebras, on concreteBanach algebras, and on related areas of analysis. Some areasthat will be emphasized in the talks include automatic continuity,amenability and Banach homology, structure of Banach algebras,spectral theories and operator theory, group algebras and otherconvolution algebras, and complex analytic methods.One of the great accomplishments of modern mathematics is abstraction.Much like the way elementary algebra generalizes arithmetic, abstractiongives mathematicians the power to solve not only individual problems,but entire classes of problems. One of the most important twentieth-century examples is the field called functional analysis. Functionalanalysis uses new abstract techniques to treat problems that had beenstudied for more than two hundred years by what we now call classicalanalysis, which is the collection of methods that grew out of the calculus.Functional analysis, instead of concentrating on individual functions,studies spaces of functions and abstractions of such spaces. Not onlycould new problems and previously intractable old problems be solved bycombining the new and old methods, but the new structures of functionalanalysis also provided a new language which was needed to express many ofthe results of modern physics and, later, of other areas of science andof economics. The spaces considered by functional analysis all have somesort of operation of addition, but many of the most important spaces haveother operations as well. In particular, Banach algebras and relatedareas involve the very large and important collection of problems andstructures which have some sort of multiplication as well as the usualaddition. By the 1960s, Banach algebras, the subject of the conference, had become a recognized field of mathematics. Since 1974 the regularinternational conferences on Banach algebras have become an importantway for researchers worldwide to keep abreast of the field, to initiateand continue research collaborations, and to exchange ideas with researchersin related areas.