This special issue is dedicated to the memory of Jean Bourgain. Bourgain was undoubtedly one of the most outstanding mathematicians of our time. His achievements, vision, and insight united many distant and very diverse directions of mathematics into one enormously powerful and broad entity. He made fundamental contributions to many fields of mathematics, including harmonic analysis, spectral theory, nonlinear partial differential equations, ergodic theory, the geometry of Banach spaces, analytic number theory, complexity, and additive combinatorics, shaping our understanding of these fields.
Many of his contributions were directly related to analytic mathematical physics, and many more developed techniques in the other fields that proved very influential. It would be impossible to give here even a brief summary of his contributions to and impact on mathematical physics. Just the number of very long standing problems Bourgain has solved can be counted in the dozens, and this would take a whole book to describe.
Jean Bourgain received his Ph.D. in 1977 and his Habilitation in 1979, both from the Free University of Brussels where he also served as a Professor from 1981 until 1985. He was a Professor at University of Illinois, Urbana-Champaign from 1985 to 2006, and at the Institut des Hautes Études Scientifiques from 1985 to 1995. In 1994, he was appointed a Professor at the Institute for Advanced Study, a position he held until his death in 2018.
The work of Jean Bourgain has been recognized by many awards, including the Salem Prize (1983), the Ostrowski Prize (1991), the Fields Medal (1994), the Shaw Prize (2010), the Crafoord Prize (2012), the Breakthrough Prize (2017), the Steele Prize (2018), and many others. He was invited to give talks at three International Congresses of Mathematicians, two International Congresses on Mathematical Physics, and two European Mathematical Congresses. He also received honorary doctorates and memberships to numerous national academies of sciences.
This volume contains papers by leading researchers in the areas of mathematical physics in which Jean Bourgain worked. The topics are diverse, ranging from spectral theory of Schrödinger operators to nonlinear wave and Schrödinger equations to geometry of nodal sets, and this reflects the unprecedented impact and diversity of profound contributions that Jean Bourgain made to many areas of mathematical physics.1–18