Biographical Sketch

I grew up in Champaign-Urbana on the Illinois prairie, and was in the first batch of students to pass through Max Beberman's exciting "new math" program for good students with good teachers, before it was eviscerated to serve a mass audience. Arithmetic had always been my weakest subject, but late in high school David Page and W. W. Sawyer opened my eyes to the beauty and logic of abstract math. I did my undergraduate work at a small liberal arts college (Reed College, in Portland), graduating in 1960. At Reed undergraduates have to write a senior thesis, and I wrote mine with John Leadley (who was working in nonassociative algebras) on Jordan algebras in characteristic 2, showing that the usual linear definition excluded the "right" algebras and admitted only the "wrong sort." It is completely coincidental that later stages of my career were concerned with quadratic Jordan algebras in characteristic 2. I did my graduate work under Nathan Jacobson at Yale, getting a Ph.D. in 1965. My final year as graduate student was spent visiting the University of Chicago during an "algebra year" 1964-65 featuring a galaxy of algebraic luminaries: N. Jacobson. A.A. Albert, I. Kaplansky. I. N. Herstein, S. A. Amitsur, P. Cohn, R. D. Schafer, D. Zelinsky. I spent two postdoctoral years at M.I.T. working with Richard Schafer (as AFOSR Postdoctoral Fellow in 1965, and C.L.E. Moore Instructor in 1966). I came to the University of Virginia as a member of the Center for Advanced Studies in 1967, and have stayed here ever since, becoming an associate professor in 1968 and professor in 1972. I served (a sentence?) as chairman of the department during 1972-75. I was a Sloan Fellow, gave an address as the International Congress of Mathematicians in Vancouver in 1974, and spent a sabbatical year in Vancouver in 1975 working with Ottmar Loos. I was a Humboldt Fellow in 1977 at the University of Muenster, Germany, under the tutelage of Max Koecher. I spent the year 1984 in Munich working with Kurt Meyberg, and the year 1990 visiting Ottawa, Bombay, and Oxford. Since 1982 I have been one of the three/four co-organizers of the international conference on Jordan theory held every three/four years in Oberwolfach, Germany.

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