Michael Aschbacher
Encyclopedia
Michael George Aschbacher (born April 8, 1944) is an American
mathematician
best known for his work on finite group
s. He was a leading figure in the completion of the classification of finite simple groups
in the 1970s and 1980s. It later turned out that the classification was incomplete, because the case of quasithin group
s had not been finished. This gap was fixed by Aschbacher and Stephen D. Smith in 2004, in a pair of books comprising about 1300 pages. Aschbacher is currently the Shaler Arthur Hanisch Professor of Mathematics at the California Institute of Technology
.
Aschbacher received his B.S. at the California Institute of Technology
in 1966 and his Ph.D.
at the University of Wisconsin–Madison
in 1969. He joined the faculty of the California Institute of Technology in 1970 and became a full professor in 1976. He was awarded the Cole Prize
in 1980, and was elected to the National Academy of Sciences
in 1990. In 1992, Aschbacher was elected a Fellow of the American Academy of Arts and Sciences
. He was awarded the Rolf Schock Prize for Mathematics by the Royal Swedish Academy of Sciences
in 2011.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
best known for his work on finite group
Finite group
In mathematics and abstract algebra, a finite group is a group whose underlying set G has finitely many elements. During the twentieth century, mathematicians investigated certain aspects of the theory of finite groups in great depth, especially the local theory of finite groups, and the theory of...
s. He was a leading figure in the completion of the classification of finite simple groups
Classification of finite simple groups
In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below. These groups can be seen as the basic building blocks of all finite groups, in much the same way as the prime numbers are the basic...
in the 1970s and 1980s. It later turned out that the classification was incomplete, because the case of quasithin group
Quasithin group
In mathematics, a quasithin group is roughly a finite simple group of characteristic 2 type and width 2. Here characteristic 2 type means that its centralizers of involutions resemble those of groups of Lie type over fields of characteristic 2, and the width is roughly the maximal rank of an...
s had not been finished. This gap was fixed by Aschbacher and Stephen D. Smith in 2004, in a pair of books comprising about 1300 pages. Aschbacher is currently the Shaler Arthur Hanisch Professor of Mathematics at the California Institute of Technology
California Institute of Technology
The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
.
Aschbacher received his B.S. at the California Institute of Technology
California Institute of Technology
The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
in 1966 and his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
at the University of Wisconsin–Madison
University of Wisconsin–Madison
The University of Wisconsin–Madison is a public research university located in Madison, Wisconsin, United States. Founded in 1848, UW–Madison is the flagship campus of the University of Wisconsin System. It became a land-grant institution in 1866...
in 1969. He joined the faculty of the California Institute of Technology in 1970 and became a full professor in 1976. He was awarded the Cole Prize
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who...
in 1980, and was elected to the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
in 1990. In 1992, Aschbacher was elected a Fellow of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
. He was awarded the Rolf Schock Prize for Mathematics by the Royal Swedish Academy of Sciences
Royal Swedish Academy of Sciences
The Royal Swedish Academy of Sciences or Kungliga Vetenskapsakademien is one of the Royal Academies of Sweden. The Academy is an independent, non-governmental scientific organization which acts to promote the sciences, primarily the natural sciences and mathematics.The Academy was founded on 2...
in 2011.
Books
- Finite group theory ISBN 0-521-78675-4
- Sporadic groups ISBN 0-521-42049-0
- 3-Transposition groups ISBN 0-521-57196-0
- The finite simple groups and their classification ISBN 0-300-02449-5
- Overgroups of Sylow subgroups in sporadic groups ISBN 0-8218-2344-2