Robert L. Griess Jr.

Biosketch

Robert Griess is an algebraist interested in finitegroups, especially infinite simple groups; finiteaspects of Lie theory; vertex operator algebras and generalizations; nonassociative mathematics; integral lattices; and moonshine.
He was born in 1945 in Savannah, Georgia, grew up in the cities of Pittsburgh and nearby Glenshaw where he attended public schools K-12. At the University of Chicago, he was awarded BS in 1967, MS in 1968 and PhD in mathematics in 1971. His first job was research instructor at the University of Michigan, where he rose through the ranks to become the Richard D. Brauer Collegiate Professor of Mathematics and then John Griggs Thompson Distinguished University Professor of Mathematics. He has held visiting positions at Rutgers, Institute for Advanced Study, Yale, Ecole Normale Superieure at Rue d’Ulm in Paris, University of California Santa Cruz, National Cheng Kung University in Tainan, Taiwan; Zhejiang University in Hangzhou, China. Honors include Guggenheim Fellowship, invited lecture at the International Congress of Mathematicians in Warsaw; Matre de Recherche, CNRS, France; Dozor Visiting Fellowship in Israel; Harold R. Johnson Diversity Service Award, University of Michigan; Distinguished Chair Professor in National Cheng Kung University, Tainan, Taiwan; American Mathematical Society Steele Prize for Seminal Research; Lester P. Monts Award for Outstanding Service at the University of Michigan; memberships in American Academy of Arts and Sciences, Fellows of the American Mathematical Society, and National Academy of Sciences.

Research Interests

Robert Griess's research started in the area of pure finite group theory, especially finite simple groups. It later expanded to nite aspects of Lie theory, nonassociative systems, lattices, vertex algebra theory and aspects of
moonshine. His main topics of research, some with coauthors, are listed: (1) determination of Schur multipliers for many finitesimple groups; (2) classifcation results for finitesimple groups; group extensions; (3) construction of the
Monster, the largest sporadic group; and consequences; (4) studies of finite quasisimple subgroups of the exceptional Lie groups G2; F4;E6;E7;E8; (5) relationships between finitegroups and vertex algebras, including classifcations
of frames; studies of automorphism groups and derivations; integral forms; (6) positive defnite integral lattices, creation of some with new records for minimum norm, characterizations of some by internal properties; in a given
dimension divisible by 8, construction of many pairwise non-isometric even unimodular lattices; (6) nonassociative systems and relations to finitesimple groups; (7) moonshine paths, which make more concrete the surprising theory of McKay-Glauberman-Norton on connections between the extended E8 diagram and pairs of 2A involutions in the Monster.