Jacques Tits: August 12, 1930 -- December 5, 2021
Photo: Jean-François Dars / IHÉS

Incidence geometry as a full discipline in its own right was founded by Jacques Tits in the course of writing his habilitation thesis. It took approximately 50 years before a journal devoted to the area was established. When Innovations in Incidence Geometry was founded in 2005, Jacques was immediately willing to be honorary editor, and remained so until he passed away. Jacques supported IIG in many ways; for example the complement to his Collected Works was published here in 2018.

Jacques left a tremendous heritage and his influence is immeasurable. It was not difficult for the editors to find many people willing to write a paper in memory of this great mathematician, and the result is collected in the present volume of IIG. We thank all of the contributors for their willingness, enthusiasm and work in creating a lot of beautiful mathematics that would have pleased Jacques immensely.

This volume begins with a very interesting biography of Jacques by Franz Bingen. This contribution gives us the privilege to have a closer look at Jacques as both a person and as an exceptionally gifted mathematician. Compiling this volume also provided the opportunity to make some important results more accessible, including Jean-Yves Hée's contribution providing a new generic proof (“à la Tits”) of an old result of Deodhar and Dyer on Coxeter groups, and we invited Anne Parreau to submit an English translation of her seminal paper on nondiscrete affine buildings (originally only available in French).

The richness of Jacques's heritage is witnessed by the large variety of subjects touched on in the papers of this issue. However they have one constant factor in common: they are driven by curiosity and the determination to know. As recounted in Franz Bingen's biographical contribution to this issue, it is this same determination that led Jacques as a little boy to want to know more about the wonderful subject of mathematics, and in particular about the beautiful interplay between algebra and geometry — a connection that Jacques himself strengthened and made inseparable.

We hope that this volume provides a stimulating collection of papers in the broad range of subjects studied by Jacques and wish the reader a lot of reading pleasure and new inspiration. We thank Mathematical Sciences Publishers for their care in producing this volume and their continued support of IIG.

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