9623282 Alperin This grant supports the research of Professor R. Alperin to work on problems in the representation of finite groups on various geometric objects. In particular he wants to work on groups acting on trees, buildings and their generalizations. He hopes to use various fixed point properties as an aid in classifying certain groups with various homological or geometrical realizations. This is research in the field of group theory. Group theory can be thought of as the study of symmetry in the abstract. As such, this area has direct applications to many areas of physics and chemistry. Moreover, within the last 30 years, many connections to problems in data transmission have been solved using techniques from group theory. There are also direct connections to the error correcting codes that are vital for modern computing such as working with CD-ROM's.
