There has been renewed interest in Hopf algebras in the last several years because of the major example of quantum groups. General knowledge about Hopf algebras may be useful to those interested in quantum groups; conversely, quantum groups have introduced some new purely algebraic ideas into Hopf algebras. Independent of any connection to quantum groups, there have been many new developments in Hopf algebras, including the solution of two old conjectures. There has also been much work extending facts about group actions to actions and coactions of Hopf algebras. In addition, in light of the interest in Hopf algebra techniques in ring theory, operator algebras, and combinatorics, the field would appeal to an audience of Hopf algebraists, ring theorists, combinatorists, and operator algebraists. This project will support an NSF-CBMS Regional Research Conference in the Mathematical Sciences on Hopf Algebras and Their Actions on Rings to be held August 11-15, 1992 at DePaul University. Professor Susan Montgomery of the University of Southern California will be the principal lecturer. To stimulate interest and activity in mathematical research, the National Science Foundation each year supports a number of NSF-CBMS Regional Research Conferences in the Mathematical Sciences. Each five-day conference features a distinguished lecturer who delivers ten lectures on a topic of important current research in one sharply focused area of the mathematical sciences. The lecturer subsequently prepares an expository monograph based upon these lectures, which is normally published by the American Mathematical Society or the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Institute of Mathematical Statistics. Certain features differentiate these conferences from typical research conferences. These are: (1) Focus on a single important and timely area of research by a leading practitioner, (2) Continued effect and local stimulation through regional emphasis, (3) Panel review for quality, breadth, and timeliness, and (4) Published monographs for a wider audience.
