BOURGAIN, JEAN

born Feb. 28, 1954, Ostend, Belg. Belgian mathematician who was awarded the Fields Medal in 1994 for his work in analysis. Bourgain received a Ph.D. from the Free University of Brussels (1977). He held appointments at the Free University (198185); jointly at the University of Illinois, Urbana-Champaign (U.S.), and the Institute of Advanced Scientific Studies, Bures-sur-Yvette, France (198594); and since 1994 at the Institute for Advanced Study, Princeton, N.J., U.S. Bourgain received the Fields Medal at the International Congress of Mathematicians in Zrich, Switz., in 1994, where his achievements in several fields were highlighted: advances in the problem of determining how large a section of a Banach space of finite dimension n can be found that resembles a Hilbert subspace; a proof of Luis Antonio Santal's inequality; a new approach to some problems in ergodic theory; results in harmonic analysis and classical operators; and nonlinear partial differential equations. Bourgain's work was noteworthy for the versatility it displayed in applying ideas from wide-ranging mathematical disciplines to the solution of diverse problems. Bourgain's publications include New Classes of Lp-Spaces (1981) and, with A. Casazza, J. Lindenstrauss, and L. Tzafriri, Banach Spaces with a Unique Unconditional Basis, up to Permutation (1985).