Robert Griess (mathematician)

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Robert Griess, Oberwolfach 2005

Robert Louis Griess junior (born October 10, 1945 in Savannah , Georgia ) is an American mathematician who deals with the theory of finite groups and is one of the discoverers (with Bernd Fischer ) of the " monsters " called finite simple group.

life and work

Griess went to school in Pittsburgh , studied at the University of Chicago (Bachelor 1967, Master 1968) and received his doctorate there in 1971 under John Griggs Thompson ( Schur multipliers of the known finite simple groups ). From 1971 he was at the University of Michigan , first as Hildebrandt Instructor, from 1973 as Assistant Professor, 1976 Associate Professor and 1981 as a full professor. In 1979/80, 1981 and 1994 he was at the Institute for Advanced Study . He was also visiting professor at Yale , at Rutgers University , at the University of California, Santa Cruz , at theÉcole normal supérieure (1986/87 as Maître de recherche of the CNRS ) and at the Chinese Zhejiang University and the National Cheng Kung University in Taiwan.

In 1981/82 he was a Guggenheim Fellow. He is a member of the American Academy of Arts and Sciences . In 1983 he was invited speaker at the ICM in Warsaw ( The sporadic simple groups and construction of the Monster ).

Griess is known for his construction of the "Monster" (also called "Friendly Giant" by him), the largest sporadic simple group as a representation in an algebra of matrices on a 196883-dimensional vector space over the rational numbers, the "Griess Algebra" . The existence of the monster was assumed from group-theoretical considerations independently of Griess and Bernd Fischer 1973, but only the explicit construction provided evidence of existence. As part of the construction, many more (twenty) previously discovered sporadic groups found their place, so that this can also be understood as a kind of unified theory of sporadic simple groups. This leaves a product structure invariant and uses the leech grid. The possibility of constructing such a representation was by no means assured at the end of 1979, when Griess carried out his research in this regard, given the high order of the monster.

Griess also participated in the classification of the finite subgroups of the exceptional Lie groups and examined vertex operator algebras.

In 2010 he received the Leroy P. Steele Prize . He is a Fellow of the American Mathematical Society and has been a member of the National Academy of Sciences since 2020 .

Fonts

  • The friendly giant. Inventiones Mathematicae , Vol. 69, 1982, pp. 1-102, online .
  • Twelve sporadic groups. Springer 1998.
  • The construction of as automorphisms of a 196.883 dimensional algebra , Proceedings National Academy of Sciences, Vol. 78, 1981, pp. 686-691, online, PDF file

literature

  • Mark Ronan: Symmetry and the Monster. Oxford University Press, 2006 (Reviewed by Griess in the Notices of the AMS, February 2007, PDF file )

Web links

Individual evidence

  1. ↑ announced in the Conference on Finite Groups, Park City, Utah 1975
  2. ↑ announced by Griess by e-mail on January 14, 1980
personal data
SURNAME Griess, Robert
ALTERNATIVE NAMES Griess, Robert Louis junior (full name); Griess, Robert L.
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH October 10, 1945
PLACE OF BIRTH Savannah , Georgia