Jean-Christophe Yoccoz

Jean-Christophe Yoccoz (29 May 1957 - 3 September 2016) was a French mathematician and one of the leading figures in the theory of dynamical systems. He won a silver medal for France at the 1973 International Mathematical Olympiad and a gold medal in 1974 (ranked 1st with 40 points), entered the École normale supérieure in 1975, and completed his doctorate in 1985 under Michael Herman. He was awarded the Fields Medal in 1994 at the ICM in Zürich, held the statutory chair of Differential equations and dynamic systems at the Collège de France from 1997 until his death, and was a member of Bourbaki.

Notes1

• Died 3 September 2016 in Paris aged 59; the Collège de France tribute was co-signed by Alain Connes, Étienne Ghys and Pierre-Louis Lions, and the IMU and IMPA both published memorials - a measure of his standing across the French and international mathematics communities.Sep 5, 2016
• Elected to the French Academy of Sciences and the Brazilian Academy of Sciences in 1994, named a chevalier of the Légion d'honneur in 1995, and a member of Bourbaki - recognition arriving in the same year as the Fields Medal.1994
• Won silver for France at the 1973 International Mathematical Olympiad (rank 7, 32/42 points) and gold at the 1974 IMO (rank 1, a perfect 40/40) as a Lycée Louis-le-Grand pupil - the earliest marker of the mathematician who would take a Fields Medal two decades later.Jul 1974
• Led a statutory chair ('Équations différentielles et systèmes dynamiques') at the Collège de France from 1996/1997 until his death in 2016, making the Collège the institutional home of his mature work.1997
• Completed his doctorate in 1985 under Michael Herman at the Centre de mathématiques Laurent-Schwartz, improving Herman's results on circle diffeomorphisms with simpler proofs and weaker hypotheses - announcing the style (geometric intuition plus combinatorial method) that defined his career.1985
• Served his alternative national service at IMPA in Brazil (1981-1983), the origin of a lifelong Brazilian tie: Brazil elected him to its Academy of Sciences in 1994 and gave him the Grand Cross of the National Order of Scientific Merit in 1998, and IMPA later published his obituary titled 'A Frenchman with a Brazilian heart'.1983
• Topped the entrance examinations for both the École Normale Supérieure and the École Polytechnique in 1975, then placed joint-first in the agrégation de mathématiques in 1977 - first in the national cohort before producing any research.1977
• Served on the ICTP Scientific Council from 2004-2013 and was a TWAS fellow from 2004, evidence that his influence ran through international research governance, not only his own theorems.2004
• Developed the 'Yoccoz puzzle', a combinatorial method for studying Julia and Mandelbrot sets; it became his most widely cited named contribution and the entry point to complex dynamics for a generation of students.1994
• Supervised doctoral students including Sylvain Crovisier and Ricardo Perez-Marco, seeding the next generation of dynamical-systems researchers.2016
• Douady's Fields Medal citation notes Yoccoz 'spends half a day on mathematical experiments, by hand or by computer', pursuing not just results but 'the manner in which it unfolds' - a computational-experimental streak unusual among pure dynamicists of his generation.1994
• Douady described him as combining 'acute geometric intuition, an impressive command of analysis, and a penetrating combinatorial sense to play the chess game at which he excels' - the chess metaphor matching his reported love of the game.1994