Jacques Tits: '(Euvres. Collected Works, Vols. Ⅰ-Ⅳ'. Edited by Francis Buekenhout, Bernhard Matthias Muhlherr, Jean-Pierre Tignol, Hendrik Van Maldeghem EMS, 2013,3963 pp.

摘要

Jacques Tits is one of the outstanding mathematicians of our time. His published (and unpublished) works, most of which are collected in these impressive four volumes, encompass a wide area of modern mathematics. The central and recurring topics in his oeuvre are certainly group theory and geometry. However, group theory itself is a vast area. During the last six decades, Jacques Tits has contributed important results to finite group theory, to Lie theory, to algebraic group theory, to combinatorial and geometric group theory, to Kac-Moody theory, and to arithmetic geometry. Probably he is one of the few present-day mathematicians who may claim to have an overview of group theory in its entirety. In some of these areas, he was among those who laid the foundations, while in others, he pushed existing results much further. The task to describe what is in these four volumes is thus somewhat intimidating. I will try to highlight and describe some of their contents, led partially by my own mathematical interests and knowledge. The four volumes group his work, of course, in a chronological order. In what follows, I will try to group some of Tits' contributions by their topics.