Robert Griess

Robert Griess
Born	(1945-10-10) October 10, 1945 (age 80) Savannah, GA, U.S.
Alma mater	University of Chicago (B.S., 1967; M.S., 1968; Ph.D., 1971)
Known for	Classification 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  (1971)
Doctoral advisor	John Griggs Thompson
Website	www.math.lsa.umich.edu/~rlg/

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]

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, with emphasis on constructions of the monster group. ^{[5] [6]}

Monster group

In 1982, Robert Griess published the first construction of the largest sporadic group, the monster group ${\displaystyle \mathbb {M} }$ (or ${\displaystyle F_{1}}$). He first successfully constructed this group while at the Institute for Advanced Study (1979–80, 1981, and later in 1994), through rotations of an object in 196,883-dimensional space. ^[7]

Originally, Griess called the monster group the "Friendly Giant"; ^[8] however, a paper published in 1979 by John Horton Conway and Simon P. Norton in the Bulletin of the London Mathematical Society titled "Monstrous Moonshine" formally coins the term. ^[9] Bernd Fischer and Griess independently predicted the existence of the monster group earlier in the decade, by 1973. ^[7]

Conway, speaking about the monster group on one occasion, expressed Griess' dissatisfaction with his choice in naming the Fischer-Griess 196,883-dimensional group, as the Monster group: ^[10]

By the way, Griess criticized me very strongly for using the term 'monster' for it, ... I wrote a postcard to Fischer, who is the first discoverer of the Monster, saying something like, 'I've been thinking a lot about your monster group'... he liked that name, and ever since then, it's been called 'the Monster' [...] Griess made the point — and I agree with him in a way — that to call it a 'monster' suggests it's sort of 'ugly', or 'frightening', or something; and I wasn't thinking of that at all, I was just thinking of it as being tremendously big! You know...maybe a bit frightening in a way, but not ugly, really a beautiful thing...

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]

Recognition

In 1983 Griess 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, as the largest of these geometric groups. ^[11] In 2010, he was awarded the AMS Leroy P. Steele Prize for Seminal Contribution to Research for his construction of the monster group. ^{[12] [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. ^{[13] [14]} In 2020 he became a member of the National Academy of Sciences. ^[15] Since 2006, Robert Griess has been an editor for Electronic Research Announcements of the AIMS (ERA-AIMS), a peer-review journal. ^[16]

Selected publications

Books

• Griess, Robert L. Jr. (1998). Twelve Sporadic Groups. Berlin: Springer-Verlag. ISBN   978-3-540-62778-4. MR   1707296. OCLC   38910263. Zbl   0908.20007. ^[17]
• Griess, Robert L. Jr. (2011). An Introduction to Groups and Lattices: Finite Groups and Positive Definite Rational Lattices. Advanced Lectures in Mathematics. Vol. 15. Somerville, MA: International Press. ISBN   978-1-57146-206-0. MR   2791918. OCLC   702615699. Zbl   1248.11048.

Journal articles

• Griess, Robert L. Jr. (1982). "The Friendly Giant" (PDF). Inventiones Mathematicae . 69: 1–102. Bibcode:1982InMat..69....1G. doi:10.1007/BF01389186. hdl:2027.42/46608. MR   0671653. Zbl   0498.20013.

• Gilman, Robert H.; Griess, Robert L. Jr. (1983). "Finite groups with standard components of Lie type over fields of characteristic two" (PDF). Journal of Algebra . 80 (2): 383–516. doi:10.1016/0021-8693(83)90007-8. hdl: 2027.42/25314 . MR   0691810. Zbl   0508.20010.

• Griess, Robert L. Jr.; Ryba, A. J. E. (1999). "Finite Simple Groups which Projectively Embed in an Exceptional Lie group are Classified!" (PDF). Bulletin of the American Mathematical Society . 36 (1): 75–93. doi:10.1090/S0273-0979-99-00771-5. MR   0165317. Zbl   0916.22008.

• Griess, Robert L. Jr. (2003). "Positive definite lattices of rank at most 8" (PDF). Journal of Number Theory . 103 (1): 77–84. doi: 10.1016/S0022-314X(03)00107-0 . MR   2008067. Zbl   1044.11014.

• Griess, Robert L. Jr.; Lam, Ching Hung (2011). "A moonshine path from E8 to the Monster" (PDF). Journal of Pure and Applied Algebra . 215 (5): 927–948. doi: 10.1016/j.jpaa.2010.07.001 . MR   2747229. Zbl   1213.17028.

• Griess, Robert L. Jr. (2012). "Moonshine paths and a VOA existence proof of the Monster". Recent developments in Lie algebras, groups and representation theory . Proc. Sympos. Pure Math. Vol. 86. Providence, RI: Amer. Math. Soc. pp. 165–172. doi:10.1090/pspum/086. ISBN   978-0-8218-6917-8. MR   2977002. Zbl   1320.20018.

• Dong, Chongying; Griess, Robert L. Jr. (2012). "Integral forms in vertex operator algebras which are invariant under finite groups". Journal of Algebra . 365 (3): 184–198. arXiv: 1201.3411 . MR   2928458. Zbl   0613.17012.

References

1. Griess, Robert L. Jr. (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 . doi:10.1090/CONM/753/15167. ISBN   978-1-4704-4938-4. 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, Robert L. Jr. (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 . 78 (1): 68–71. doi: 10.1090/S0002-9904-1972-12855-6 . JSTOR   1996474. MR   2611672. 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 . Zbl   1482.20010.
6. Griess, Robert L. Jr. (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. Zbl   1537.20002. Archived (PDF) from the original on 2023-01-22.
7. Siobhan Roberts (2013). "Curiosities: Pursuing the Monster". IAS (Ideas) . Institute for Advanced Study.
8. Griess, Robert L. Jr. (1982). "The Friendly Giant". Inventiones Mathematicae. 69: 91. Bibcode:1982InMat..69....1G. doi:10.1007/BF01389186. hdl: 2027.42/46608 . MR   0671653.
9. Conway, John H.; Norton, Simon P. (1979). "Monstrous Moonshine" . Bulletin of the London Mathematical Society. 11 (3). London Mathematical Society: 308–339. Quote: We proposed to call this group the MONSTER and conjectured that it had a representation of degree 196883... (p. 308).
10. Alex Ryba, with John H. Conway (interviewee) (May 12, 2011). Siobhan Roberts, ed. 19. The Monster (Video interview). John Conway (1937 - 2020) (ScienceLives). New York City: Simons Foundation. Event occurs at 05:07 − 05:58. Retrieved 2025-11-20. YouTube:...McOH5o
11. "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."
12. "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)."

13. "Robert L. Griess (Member)". American Academy of Arts & Sciences. Retrieved 2023-01-02.
14. "List of Fellows of the American Mathematical Society". American Mathematical Society. Retrieved 2013-01-19.
15. "National Academy of Sciences Elects New Members". National Academy of Sciences. April 27, 2020. Retrieved 2023-01-02.
16. "Editorial Board". Electronic Research Announcements. American Institute of Mathematical Sciences. ISSN   1935-9179 . Retrieved 2023-01-07.
17. 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.

External links

• Robert Griess at the Mathematics Genealogy Project
• Robert Griess: My life and times with the sporadic simple groups on YouTube for the Mathematical Science Literature lecture series, Harvard University (2020)