This year’s Abel Prize has gone to topologist Dennis Sullivan, for the announcement see here, with more information about Sullivan and his work here. There are press stories at Nature, the New York Times, Quanta, and elsewhere.
Sullivan was one of the leading figures in great advances in understanding the topology of manifolds in higher dimensions during the late 60s and 70s. Some of the best of his early work for many years was only available if you could find a copy of unpublished mimeographed notes from a 1970 MIT course. In 2005 a Tex’ed version of the notes was finally published (available here). This includes as a postscript Sullivan’s own description of this work, how it came about, and how it influenced his later work.
This was followed by wonderful work on rational homotopy theory, making use of differential forms. For this, see Sullivan’s 1977 Infinitesimal computations in topology, and lecture notes on this by Phil Griffiths and John Morgan. In later years Sullivan’s attention turned to subjects with which I’m not very familiar: topics in dynamical systems and the development of what he called “string topology”.
Since 1981 Sullivan has held the Einstein chair at the CUNY Graduate Center here in NYC, running a seminar each week that concentrates on the relation between topology and QFT. For many years these were held in a Russian style, going on for multiple hours, possibly with a break, until all participants were exhausted. There’s a remarkable collection of videos of these lectures at the seminar site, including many going way back into the 80s and 90s, with video recorded at a time when this was quite unusual (more recent ones are on Youtube).
When I first came to Columbia Sullivan was often here attending and giving lectures, for many years splitting his time between Paris (where he held a position at the IHES), New York and Rio. The Abel Prize biography explains
In 1981, Sullivan was made the Albert Einstein Chair in Science (Mathematics) at the Graduate School and University Center of The City University of New York. He kept his position at IHES and spent the next decade and a half shuttling between Paris and New York, often on Concorde.
Some of the various stories I heard about Sullivan’s lifestyle at the time involved his having multiple apartments in New York, which he used to host a variety of visiting mathematicians. Another story I heard directly from him was about how he survived an attempted car-jacking in Brazil, during which he was shot, but managed to escape and drive himself to a hospital for treatment. I had first heard about this from Mike Hopkins several years before. When I asked Hopkins why he had become a topologist, he said that one factor was the inspiring example of people like Sullivan who worked in the field, jokingly characterizing it as involving “real men who got into gun-fights”.
In 1997 Sullivan traded the IHES position for one at Stony Brook, and over the years has unfortunately been seen less often here at Columbia. Congratulations to him on the well-deserved prize!