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 | October 10, 1945 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
editGriess 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
editGriess' 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
editBooks
edit- 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
edit- 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
edit- ^ 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.
- ^ "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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ "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."
- ^ 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.
- ^ "Robert L. Griess (Member)". American Academy of Arts & Sciences. AAA&S. Retrieved 2023-01-02.
- ^ "List of Fellows of the American Mathematical Society". American Mathematical Society. AMS. Retrieved 2013-01-19.
- ^ "National Academy of Sciences Elects New Members". National Academy of Sciences. NAS. April 27, 2020. Retrieved 2023-01-02.
- ^ "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
- ^ "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)."
- ^ 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
edit- 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)