This award supports five U.S. mathematicians for collaborative research in group theory with a number of German mathematicians at several universities in the Federal Republic of Germany (FRG). The collaborative framework was organized by Professor Stephen D. Smith of the University of Illinois at Chicago and Professors Franz G. Timmesfeld of the University of Geissen and Gernot Stroth of the Free University, Berlin. The proposed visits will permit continuation of some highly productive collaborative relationships previously supported by the U.S.-FRG Program, while also introducing some new participants. Reciprocal visits by the Germans to several U.S. universities are being supported by the DFG (the German equivalent of NSF.) The various partnerships among the two groups will focus on several closely related problems: axiomatization and classification of geometries for simple groups, universal covers of finite geometries, the theory of trees and more general amalgams for geometric groups; and the application of such results to the study of maximal subgroups and representation of simple groups. Most of the leaders in this area of mathematics are working in the U.S. and West Germany, so fruitful collaboration is expected. Both geometry and group theory have important applications in twentieth century science - for example, geometry in the physics of relativity, and group theory in physics and chemistry at the quantum and particle levels. Natural interrelations between the two theories have long been studied. The use of techniques from discrete geometry in problems of finite group theory is a particularly vigorous area of modern mathematical research.
