Robert Griess

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Robert Griess
Robert Griess.jpg
Born (1945-10-10) October 10, 1945 (age 78)
NationalityAmerican
Alma mater University of Chicago (B.S., 1967; M.S., 1968; Ph.D., 1971)
Known forClassification of sporadic groups (Happy Family and pariahs)
Construction of the Fischer–Griess Monster group
Gilman–Griess theorem
Griess algebra
Awards Leroy P. Steele Prize (2010)
Scientific career
Fields Mathematics
Institutions University of Michigan
Thesis Schur Multipliers of the Known Finite Simple Groups  (1972)
Doctoral advisor John Griggs Thompson

Robert Louis Griess, Jr. (born 1945, Savannah, Georgia) is a mathematician working on finite simple groups and vertex algebras. [1] He is currently the John Griggs Thompson Distinguished University Professor of mathematics at University of Michigan. [2]

Contents

Education

Griess developed a keen interest in mathematics prior to entering undergraduate studies at the University of Chicago in the fall of 1963. [3] There, he eventually earned a Ph.D. in 1971 after defending a dissertation on the Schur multipliers of the then-known finite simple groups. [4]

Career

Griess' work has focused on group extensions, cohomology and Schur multipliers, as well as on vertex operator algebras and the classification of finite simple groups. [5] [6] In 1982, he published the first construction of the monster group using the Griess algebra, and in 1983 he was an invited speaker at the International Congress of Mathematicians in Warsaw to give a lecture on the sporadic groups and his construction of the monster group. [7] In the same landmark 1982 paper where he published his construction, Griess detailed an organization of the twenty-six sporadic groups into two general families of groups: the Happy Family and the pariahs. [8]

He became a member of the American Academy of Arts and Sciences in 2007, and a fellow of the American Mathematical Society in 2012. [9] [10] In 2020 he became a member of the National Academy of Sciences. [11] Since 2006, Robert Griess has been an editor for Electronic Research Announcements of the AIMS (ERA-AIMS), a peer-review journal. [12]

In 2010, he was awarded the AMS Leroy P. Steele Prize for Seminal Contribution to Research for his construction of the monster group, which he named the Friendly Giant . [13]

Selected publications

Books

Journal articles

Related Research Articles

<span class="mw-page-title-main">Monster group</span> Sporadic simple 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
   808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000
   = 246 · 320 · 59 · 76 · 112 · 133 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71
   ≈ 8×1053.

<span class="mw-page-title-main">Simple group</span> Group without normal subgroups other than the trivial group and itself

In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, namely a nontrivial normal subgroup and the corresponding quotient group. This process can be repeated, and for finite groups one eventually arrives at uniquely determined simple groups, by the Jordan–Hölder theorem.

<span class="mw-page-title-main">Baby monster group</span> Sporadic simple group

In the area of modern algebra known as group theory, the baby monster groupB (or, more simply, the baby monster) is a sporadic simple group of order

<span class="mw-page-title-main">Sporadic group</span> Finite simple group type not classified as Lie, cyclic or alternating

In the mathematical classification of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic finite groups, or just the sporadic groups.

<span class="mw-page-title-main">Suzuki sporadic group</span> Sporadic simple group

In the area of modern algebra known as group theory, the Suzuki groupSuz or Sz is a sporadic simple group of order

<span class="mw-page-title-main">Higman–Sims group</span> Sporadic simple group

In the area of modern algebra known as group theory, the Higman–Sims group HS is a sporadic simple group of order

<span class="mw-page-title-main">O'Nan group</span> Sporadic simple group

In the area of abstract algebra known as group theory, the O'Nan groupO'N or O'Nan–Sims group is a sporadic simple group of order

<span class="mw-page-title-main">Rudvalis group</span> Sporadic simple group

In the area of modern algebra known as group theory, the Rudvalis groupRu is a sporadic simple group of order

<span class="mw-page-title-main">Group of Lie type</span>

In mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field. The phrase group of Lie type does not have a widely accepted precise definition, but the important collection of finite simple groups of Lie type does have a precise definition, and they make up most of the groups in the classification of finite simple groups.

Robert Arnott Wilson is a retired mathematician in London, England, who is best known for his work on classifying the maximal subgroups of finite simple groups and for the work in the Monster group. He is also an accomplished violin, viola and piano player, having played as the principal viola in the Sinfonia of Birmingham. Due to a damaged finger, he now principally plays the kora.

Robert Steinberg was a mathematician at the University of California, Los Angeles.

Mathieu group M<sub>12</sub> Sporadic simple group

In the area of modern algebra known as group theory, the Mathieu groupM12 is a sporadic simple group of order

<span class="mw-page-title-main">Pariah group</span> Sporadic group that is not a subquotient of the monster

In group theory, the term pariah was introduced by Robert Griess in Griess (1982) to refer to the six sporadic simple groups which are not subquotients of the monster group.

<span class="mw-page-title-main">Bernd Fischer (mathematician)</span> German mathematician (1936–2020)

Bernd Fischer was a German mathematician.

Koichiro Harada is a Japanese mathematician working on finite group theory.

Fischer group Fi<sub>24</sub> Sporadic simple group

In the area of modern algebra known as group theory, the Fischer groupFi24 or F24 or F3+ is a sporadic simple group of order

Conway group Co<sub>2</sub> Sporadic simple group

In the area of modern algebra known as group theory, the Conway groupCo2 is a sporadic simple group of order

Conway group Co<sub>3</sub> Sporadic simple group

In the area of modern algebra known as group theory, the Conway group is a sporadic simple group of order

Conway group Co<sub>1</sub> Sporadic simple group

In the area of modern algebra known as group theory, the Conway groupCo1 is a sporadic simple group of order

References

  1. Griess, Jr., Robert L. (2020). "Research topics in finite groups and vertex algebras". Vertex Operator Algebras, Number Theory and Related Topics. Contemporary Mathematics. Vol. 753. Providence, Rhode Island: American Mathematical Society. pp. 119–126. arXiv: 1903.08805 . Bibcode:2019arXiv190308805G. doi:10.1090/CONM/753/15167. ISBN   9781470449384. S2CID   126782539. Zbl   1490.17034.
  2. "Griess Named Distinguished University Professor". University of Michigan College of Literature, Science, and the Arts. University of Michigan. May 20, 2016. Retrieved 2023-01-02.
  3. Griess, Jr., Robert L. (2010-08-18). "Interview with Prof. Robert Griess". Interviews in English (Interview). Interviewed by Shun-Jen Cheng and company. New Taipei: Institute of Mathematics, Academia Sinica . Retrieved 2023-01-07.
  4. Griess, Robert L. (1972). "Schur Multipliers of the Known Finite Simple Groups" (PDF). Bulletin of the American Mathematical Society (Ph.D. Thesis). 78 (1): 68–71. doi: 10.1090/S0002-9904-1972-12855-6 . JSTOR   1996474. MR   2611672. S2CID   124700587. Zbl   0263.20008.
  5. Smith, Stephen D. (2018). "A Survey: Bob Griess' work on Simple Groups and their Classification" (PDF). Bulletin of the Institute of Mathematics. 13 (4). Academia Sinica (New Series): 365–382. doi: 10.21915/BIMAS.2018401 . S2CID   128267330. Zbl   1482.20010.
  6. Griess, Jr., Robert L. (2021). "My life and times with the sporadic simple groups". Notices of the International Consortium of Chinese Mathematicians. 9 (1): 11–46. doi: 10.4310/ICCM.2021.v9.n1.a2 . ISSN   2326-4810. S2CID   239181475. Zbl   07432649. Archived (PDF) from the original on 2023-01-22.{{cite journal}}: CS1 maint: Zbl (link)
  7. "Proceedings of the International Congress of Mathematicians, August 16-24, 1983, Warszawa" (PDF). International Mathematical Union. IMU. pp. 369–384. Retrieved 2023-01-02. Lecture on "The sporadic simple groups and construction of the monster."
  8. Griess, Jr., Robert L. (1982). "The Friendly Giant". Inventiones Mathematicae. 69: 91. Bibcode:1982InMat..69....1G. doi:10.1007/BF01389186. hdl: 2027.42/46608 . MR   0671653. S2CID   264223009.
  9. "Robert L. Griess (Member)". American Academy of Arts & Sciences. AAA&S. Retrieved 2023-01-02.
  10. "List of Fellows of the American Mathematical Society". American Mathematical Society. AMS. Retrieved 2013-01-19.
  11. "National Academy of Sciences Elects New Members". National Academy of Sciences. NAS. April 27, 2020. Retrieved 2023-01-02.
  12. "Editorial Board". Electronic Research Announcements. American Institute of Mathematical Sciences (AIMS). ISSN   1935-9179 . Retrieved 2023-01-07. Previously published by the AMS, ISSN   1079-6762
  13. "2010 Steele Prizes" (PDF). Notices of the American Mathematical Society. 57 (4): 511–513. April 2010. ISSN   0002-9920.
    "To Robert L. Griess Jr. for his construction of the 'Monster' sporadic finite simple group, which he first announced in 'A construction of F1 as automorphisms of a 196,883-dimensional algebra' (Proc. Nat. Acad. Sci. U.S.A. 78 (1981), no. 2, part 1, 686-691) with details published in 'The friendly giant' (Invent. Math. 69 (1982), no. 1, 1-102)."
  14. Conder, Marston (December 2003). "Review: Twelve Sporadic Groups, by Robert L. Griess, Jr." (PDF). Newsletter of the New Zealand Mathematical Society . 89: 44–45. ISSN   0110-0025.