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Steve Chaplin
IU Communications

Last modified: Wednesday, January 9, 2013

IU Distinguished Professor Larsen receives Moore Prize from American Mathematical Society

Honor is for producing most outstanding research article in past six years

Jan. 9, 2013

BLOOMINGTON, Ind. -- Michael Larsen, an Indiana University Distinguished Professor in the College of Arts and Sciences' Department of Mathematics, has received the E.H. Moore Research Article Prize from the American Mathematical Society.

Michael Larsen

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Michael Larsen

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Awarded every three years for an outstanding research article that appeared in the past six years in one of the primary research journals of the American Mathematical Society, the Moore Prize was established in 2002 in honor of E.H. Moore, founder of the Chicago branch of the American Mathematical Society and the society's sixth president.

Larsen shares the prize with Richard Pink, professor of mathematics at the Swiss Federal Institute of Technology in Zurich, for their article "Finite subgroups of algebraic groups" published in the Journal of the American Mathematical Society in 2011.

"Larsen and Pink use concepts from algebraic geometry to give a classification of finite simple linear groups and thereby provide a revolutionary and influential point of view on a subject of classical interest," said Kevin Zumbrun, chair of the Department of Mathematics. "This is a brilliant and extremely original work on a problem of fundamental mathematical importance."

A group is the most basic object in abstract mathematics: a set with an operation that assigns two elements of the set a third element of the set.

"For example, the set of nonzero real numbers forms a group with the operation of ordinary multiplication," Zumbrun said. The operation must satisfy certain axioms, and a group is finite if the number of elements in the set is finite. The basic building blocks of groups are the so-called simple groups, which in fact are very complex yet termed simple because they don't break into smaller pieces.

"The classification of finite simple groups was a major achievement of the 20th century but is in some sense intellectually unsatisfying since the proof is scattered throughout 500 research articles, and its complexity is such that no individual can vouch for the veracity of all the details," added mathematics professor and previous department chair James F. Davis.

Historically there were two examples of groups: permutation groups and linear groups. The notion of an abstract group was codified in the 19th century to unify these two examples. A linear group is a set of n-by-n matrices with entries in a field k with the group operation given by matrix multiplication. Larsen and Pink showed that for every n and k, there is a number J so that every simple linear group either has less than J elements or is a group of Lie type, a discrete group modeled on an infinite continuous group.

"Their proof is understandable, is independent of the classification of finite simple groups, and in turn sheds light on the complexities of this classification," Davis said.

The Moore Prize citation said, "The article provides a conceptual proof of an approximation to the classification of finite simple groups, using methods independent of the classification." One reviewer of the paper said, "The authors have done an excellent job of presenting the deep mathematics in the paper, and the result is a profound piece of work which is accessible to non-experts."

A full professor at IU since 2001, Larsen in 2011 was promoted to the rank of distinguished professor for his work at the interface of arithmetic algebraic geometry, combinatorial group theory, combinatorics and number theory. Editor of the Indiana University Mathematics Journal and founder in 2008 of the Bloomington Math Circle, an after-school program for mathematically gifted elementary school students, Larsen earned a Bachelor of Arts from Harvard University in 1984 and a Ph.D. from Princeton University in 1988.

Larsen and Pink will receive the prize Jan. 10 in San Diego during the Joint Mathematics Meetings of the American Mathematical Society and the Mathematical Association of America.

For more information or to speak with Larsen, please contact Steve Chaplin, IU Communications, at 812-856-1896 or