9622843 Aschbacher This grant supports the research of Professor M. Aschbacher to work on three different areas in finite group theory. The first problem is to give a unified treatment of the existence and uniqueness of the finite sporadic simple groups. The next problem is to work on a complete treatment of the classification of quasithin groups. Finally, he intends to study finite group actions on certain topological and geometric objects, with special attention to Hirzebruch's prize question. 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.
