Robert Griess

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]

Robert Griess
Born	(1945-10-10) October 10, 1945 (age 79) Savannah, GA, U.S.
Nationality	American
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 (1972)
Doctoral advisor	John Griggs Thompson

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

• Griess, Jr., Robert L. (1998). Twelve Sporadic Groups. Berlin: Springer-Verlag. ISBN 9783540627784. MR 1707296. OCLC 38910263. Zbl 0908.20007.^[14]
• Griess, Jr., Robert L. (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 9781571462060. MR 2791918. OCLC 702615699. Zbl 1248.11048.

Journal articles

• Griess, Jr., Robert L. (1982). "The Friendly Giant" (PDF). Inventiones Mathematicae. 69: 1–102. Bibcode:1982InMat..69....1G. doi:10.1007/BF01389186. hdl:2027.42/46608. MR 0671653. S2CID 123597150. Zbl 0498.20013.

• Gilman, Robert H.; Griess, Jr., Robert L. (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. S2CID 119695725. Zbl 0508.20010.

• Griess, Jr., Robert L.; 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. S2CID 51774978. Zbl 0916.22008.

• Griess, Jr., Robert L. (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. S2CID 119595195. Zbl 1044.11014.

• Griess, Jr., Robert L.; 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. S2CID 123613651. Zbl 1213.17028.

• Griess, Jr., Robert L. (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, Jr., Robert L. (2012). "Integral forms in vertex operator algebras which are invariant under finite groups". Journal of Algebra. 365 (3): 184–198. arXiv:1201.3411. doi:10.1016/j.jalgebra.2012.05.006. MR 2928458. S2CID 38466335. Zbl 0613.17012.

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 1537.20002. Archived (PDF) from the original on 2023-01-22.
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.

External links

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