The Abel Prize 2013--2017 (Q1790703)

This is the third volume dedicated to the work of Abel prize winners; the first volume [Zbl 1247.01025] covered the years 2003--2007, the second [Zbl 1282.01002] the period 2008--2012, and the present volume the years 2013--2017. The recipients of the prize are Pierre Deligne (2013), Yakov G. Sinai (2014), John Nash and Louis Nirenberg (2015), Andrew Wiles (2016) and Yves Meyer (2017). Each mathematician has contributed a mathematical autobiography, and there is an additional curriculum vitae and a list of publications for each. Luc Illusie describes Deligne's work in ``Pierre Deligne: a poet of arithmetic geometry''. His early work deals with spectral sequences, duality theorems, and Hodge theory. Deligne's best-known contribution probably is his work on Weil conjectures. Among other topics he has worked on, the Weil-Deligne group, local constants of \(L\)-functions, and motives and periods are mentioned. Carlo Boldrighini and Dong Li describe Sinai's work on dynamical systems in fluid dynamics; Leonid Bunimovich explains Sinai's ideas on mathematical billiards, and F. Cellarosi gives a survey on Sinai's contributions to number theory. The next articles are by E. Gurovich (``Entropy theory of dynamical systems''), K. Khanin (``Mathematical physics''), Y. Pesin (``Sinai's work on Markov partitions and SRB measures''), N. Simányi (``Further developments of Sinai's ideas: the Boltzmann-Sinai hypothesis''), and D. Szász (``Markov approximations and statistical properties of billiards''). Sylvia Nasir describes John Nash and his life, and C. De Lellis explains ``The masterpieces of John Forbes Nash Jr.'', which seem to have been eclipsed by his work in game theory. R. V. Kohn discusses ``A few of Louis Nirenberg's many contributions to the theory of partial differential equations''. Christopher Skinner takes the readers through ``The mathematical works of Andrew Wiles'': explicit reciprocity laws, elliptic units, the Coates-Wiles theorem, Iwasawa's main conjecture, Galois representations, modular elliptic curves and Fermat's last theorem. Finally, A. Cohen takes the readers on ``A journey through the mathematics of Yves Meyes''.