Robert Louis Griess, Jr. (born 1945,
Savannah, Georgia
Savannah ( ) is the oldest city in the U.S. state of Georgia (U.S. state), Georgia and is the county seat of Chatham County, Georgia, Chatham County. Established in 1733 on the Savannah River, the city of Savannah became the Kingdom of Great Br ...
) 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 research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...
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
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.
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\;\overs ...
s,
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 it ...
and their properties. He was awarded a
Guggenheim Fellowship
Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...
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
246320597611213317192329314147 ...
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
In the area of abstract algebra known as group theory, the monster group M (also known as the Fisc ...
, for which he was awarded the 2010
AMS AMS or Ams may refer to:
Organizations Companies
* Alenia Marconi Systems
* American Management Systems
* AMS (Advanced Music Systems)
* ams AG, semiconductor manufacturer
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Educational institutions
* A ...
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
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the Nevanlinna Prize (to be rename ...
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
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...
(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, and ...
(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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See also
*
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
In the area of abstract algebra known as group theory, the monster group M (also known as the Fisc ...
*
Gilman–Griess theorem In finite group theory, a mathematical discipline, the Gilman–Griess theorem, proved by , classifies the finite simple
Simple or SIMPLE may refer to:
*Simplicity, the state or quality of being simple
Arts and entertainment
* ''Simple'' (al ...
References
External links
*
Homepageat 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