Robert Louis Griess, Jr. (born 1945,

Savannah, Georgia Savannah ( ) is the oldest city in the U.S. state of Georgia and is the county seat of Chatham County. Established in 1733 on the Savannah River, the city of Savannah became the British colonial capital of the Province of Georgia and later t ...

) is a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

working on

finite simple group Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked ...

s and

vertex algebras In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string theory. In addition to physical applications, vertex operator algebras have proven usef ...

. He is currently the John Griggs Thompson Distinguished University Professor of mathematics at

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

Education

Griess developed a keen interest in mathematics prior to entering undergraduate studies at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

in the fall of 1963. There, he eventually earned a Ph.D. in 1971 under the supervision of

John Griggs Thompson John Griggs Thompson (born October 13, 1932) is an American mathematician at the University of Florida noted for his work in the field of finite groups. He was awarded the Fields Medal in 1970, the Wolf Prize in 1992, and the Abel Prize in 2008. ...

after defending a dissertation on the

Schur multiplier In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group H_2(G, \Z) of a group ''G''. It was introduced by in his work on projective representations. Examples and properties The Schur multiplier \oper ...

s of the then-known

Research

Griess' early work focused on

group extension In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence :1\to N\;\ove ...

cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...

and Schur multipliers, as well as on the

classification of finite simple groups In mathematics, the classification of the finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or else i ...

and their properties. He was awarded a Guggenheim Fellowship in 1981. In 1982, he published the first construction of the

monster group In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group, having order 24632059761121331719232931414759 ...

using the

Griess algebra In mathematics, the Griess algebra is a commutative non-associative algebra on a real vector space of dimension 196884 that has the Monster group ''M'' as its automorphism group. It is named after mathematician R. L. Griess, who constructed it in ...

, for which he was awarded the 2010 AMS

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

for Seminal Contribution to Research. He was an invited speaker at the International Congress of Mathematicians in Warsaw in 1983 to give a lecture on his construction of the monster group, which he called the ''friendly giant''. He is a member of the National Academy of Sciences (2020) and the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, a ...

(2007). In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. Since 2006, Robert Griess has been a member of the editorial board of Electronic Research Announcements of the AIMS (ERA-AIMS), a peer-review journal.

Selected publications

Books

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Journal articles

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References

External links

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Homepage
at the Department of Mathematics at the University of Michigan {{DEFAULTSORT:Griess, Robert L. Living people 20th-century American mathematicians 21st-century American mathematicians Group theorists University of Michigan faculty Fellows of the American Mathematical Society 1945 births