PIMS Special Speaker: Configurations of points and lines - A brief survey

A k-configuration is a finite collection of n points and n lines, such that each of the n points is on precisely k lines and each line contains precisely k points. Some relevant results were known long ago, but the recent years have seen a large number of new results and novel problems. The development of the ideas will be sketched and some of the outstanding open questions described. A 3-configuration with n = 15 is shown below.