In 1990 Jones was awarded the Fields medal at the ICM at Kyoto. The ostensible reason was his discovery in 1984 of a new polynomial invariant for knots and links in 3-space. Knot theory is a rather established field, and his discovery came as a complete surprise to knot-topologists, who had been searching for new invariants for the better part of a century. Striking as such a discovery may have been, it was just a spin-off from discovering startling and hitherto unsuspected relationships between von Neumann algebras and geometric topology. At the heart of the matter lies Jones' index theorem with repercussions not only on the aforementioned knot theory but also tying together seemingly diverse fields like representations of Lie algebras, quantum groups and statistical mechanics. It is safe to claim that Jones' work along with that of Connes has been instrumental in revitalizing the subject of von Neumann algebras giving it a much vaster scope, and making it a central part of modern mathematics.
In addition to the Fields medal, he has enjoyed a variety of awards and distinctions, the complete list of which may be too tedious to list here. Suffice it to single out, among his fellowships in various prestigous societies like the Royal Society, the AASA and the National Academy of Sciences, the award of the Honorary Vice Presidency for life of the International Guild of Knot Tyers, a position he has enjoyed since 1992.
Jones is an enthusiastic sportsman, playing squash and tennis, but above all nurturing a passion for wind-surfing, occasions for which there unfortunately will be few if any during his trip to Sweden, which he nevertheless very much looks forward to.
In his tour around Sweden, he will focus on subfactors and noncommutative geometry, giving an elementary talk on the latter.
An excellent summary of Jones' scientific work, except of course being inevitably ten years out of date, was presented by Joan Birman in the proceedings of the Kyoto Congress.