Wolf Prize Laureate in Mathematics 2012
Affiliation at the time of the award:
California Institute of Technology, USA
“for being a principal architect of the classification of finite simple groups. His impact on the theory of finite is extraordinary in its depth, breadth and beauty”.
Michael Aschbacher And John Thompson (wolf prize Laureate of 1992) are the two great modern masters of the theory of finite groups, in an era that brought to fruition a line of research going back to Galois in the 1830’s. The breadth and depth of Aschbacher’s understanding of finite groups in general, and finite simple groups in particular, and the power he brought to bear on their analysis, are astonishing.
Aschbacher astounded the finite group theory community with a series of papers that raised the classification project for finite simple groups from a distant dream to the reality it is today.
In a series of papers in the 1970’s Aschbacher developed the theory of standard components and tightly embedded subgroups, and brought the theory of groups of odd characteristic type close to the completion.
Turning next to groups of characteristic type, Aschbacher handled all of the most difficult cases, notably the Thin Group case, the p-Uniqueness Case, and finally the Quasithin Case. This last result, contained in two massive monographs written jointly with S.D Smith, completed the classification of finite simple groups. In the process, he significantly advanced the theories of GF(2) representations, Thompson factorization, and pushing- up.
Also worthy of mention are Aschbacher’s work on maximal subgroups of finite simple groups, his joint work with Y.Segev on the uniqueness of the sporadic groups, and his joint work with S.D. Smith on the Quillen conjecture.