Biography:Robert Griess
Robert Griess | |
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| 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 |
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.[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. OCLC 38910263.[14]
- Griess, Jr., Robert L. (2011). An Introduction to Groups and Lattices: Finite Groups and Positive Definite Rational Lattices. Advanced Lectures in Mathematics. 15. Somerville, MA: International Press. ISBN 9781571462060. OCLC 702615699.
Journal articles
- Griess, Jr., Robert L. (1982). "The Friendly Giant". Inventiones Mathematicae 69: 1–102. doi:10.1007/BF01389186. Bibcode: 1982InMat..69....1G. https://deepblue.lib.umich.edu/bitstream/handle/2027.42/46608/222_2005_Article_BF01389186.pdf?sequence=1.
- Gilman, Robert H.; Griess, Jr., Robert L. (1983). "Finite groups with standard components of Lie type over fields of characteristic two". Journal of Algebra 80 (2): 383–516. doi:10.1016/0021-8693(83)90007-8. https://deepblue.lib.umich.edu/bitstream/2027.42/25314/1/0000759.pdf.
- Griess, Jr., Robert L.; Ryba, A. J. E. (1999). "Finite Simple Groups which Projectively Embed in an Exceptional Lie group are Classified!". Bulletin of the American Mathematical Society 36 (1): 75–93. doi:10.1090/S0273-0979-99-00771-5. https://www.ams.org/journals/bull/1999-36-01/S0273-0979-99-00771-5/S0273-0979-99-00771-5.pdf.
- Griess, Jr., Robert L. (2003). "Positive definite lattices of rank at most 8". Journal of Number Theory 103 (1): 77–84. doi:10.1016/S0022-314X(03)00107-0. http://www.math.lsa.umich.edu/~rlg/researchandpublications/pdffiles1/uniqe8.pdf.
- Griess, Jr., Robert L.; Lam, Ching Hung (2011). "A moonshine path from E8 to the Monster". Journal of Pure and Applied Algebra 215 (5): 927–948. doi:10.1016/j.jpaa.2010.07.001. http://www.math.lsa.umich.edu/~rlg/researchandpublications/pdffiles/moonshinepath13oct09.pdf.
- 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.. 86. Providence, RI: Amer. Math. Soc.. pp. 165–172. doi:10.1090/pspum/086. ISBN 978-0-8218-6917-8. http://www.ams.org/books/pspum/086/.
- 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. doi:10.1016/j.jalgebra.2012.05.006.
References
- ↑ Griess, Jr., Robert L. (2020). "Research topics in finite groups and vertex algebras". Vertex Operator Algebras, Number Theory and Related Topics. Contemporary Mathematics. 753. Providence, Rhode Island: American Mathematical Society. pp. 119–126. doi:10.1090/CONM/753/15167. ISBN 9781470449384. Bibcode: 2019arXiv190308805G.
- ↑ "Griess Named Distinguished University Professor". University of Michigan. May 20, 2016. https://lsa.umich.edu/math/news-events/all-news/search-news/griess-named-distinguished-university-professor.html.
- ↑ 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". Bulletin of the American Mathematical Society 78 (1): 68–71. doi:10.1090/S0002-9904-1972-12855-6. https://www.ams.org/journals/bull/1972-78-01/S0002-9904-1972-12855-6/S0002-9904-1972-12855-6.pdf.
- ↑ Smith, Stephen D. (2018). "A Survey: Bob Griess' work on Simple Groups and their Classification". Bulletin of the Institute of Mathematics (Academia Sinica (New Series)) 13 (4): 365–382. doi:10.21915/BIMAS.2018401. https://web.math.sinica.edu.tw/bulletin_ns/20184/2018401.pdf.
- ↑ 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. https://www.intlpress.com/site/pub/pages/journals/items/iccm/content/vols/0009/0001/a002/index.php?mode=ns.
- ↑ "Proceedings of the International Congress of Mathematicians, August 16-24, 1983, Warszawa". IMU. pp. 369–384. https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1983.1/ICM1983.1.ocr.pdf. Lecture on "The sporadic simple groups and construction of the monster."
- ↑ Griess, Jr., Robert L. (1982). "The Friendly Giant". Inventiones Mathematicae 69: 91. doi:10.1007/BF01389186. Bibcode: 1982InMat..69....1G. https://www.digizeitschriften.de/dms/img/?PPN=PPN356556735_0069&DMDID=dmdlog7.
- ↑ "Robert L. Griess (Member)". AAA&S. https://www.amacad.org/person/robert-l-griess.
- ↑ "List of Fellows of the American Mathematical Society". AMS. https://www.ams.org/profession/fellows-list.
- ↑ "National Academy of Sciences Elects New Members". NAS. April 27, 2020. https://www.nasonline.org/news-and-multimedia/news/2020-nas-election.html.
- ↑ "Editorial Board". American Institute of Mathematical Sciences (AIMS). http://eramath.s3-website-us-east-1.amazonaws.com/EditorialBoard.html. Previously published by the AMS, ISSN 1079-6762
- ↑ "2010 Steele Prizes". Notices of the American Mathematical Society 57 (4): 511–513. April 2010. ISSN 0002-9920. https://www.ams.org/notices/201004/rtx100400510p.pdf.
- "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..". Newsletter of the New Zealand Mathematical Society 89: 44–45. ISSN 0110-0025. https://nzmathsoc.org.nz/downloads/newsletters/NZMSnews89_Dec2003.pdf?1262333312.
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)
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