PIMS Distinguished Speaker:Branko Grünbaum

 A finite family of (straight) lines in the projective plane is a simplicial arrangement provided all faces (connected components of the complement) are triangles (simplices). Similarly for arrangements of (hyper) planes in higher dimensions. Starting with their first appearance in 1940, simplicial arrangements have attracted attention for their unexpected and unpredictable aspects. While originally investigated due to their extremal properties, more recently connections were found to various algebraic and combinatorial topics. Many open problems remain; most prominent among them is the question whether in all dimensions the number of sporadic (that is unsystematic) arrangements is finite. In particular, in the plane there are three infinite (systematic) families, and there are ninety-four known sporadic ones – but it is still possible that there is an infinite number of these.