Let G be a primitive permutation group on a finite set X and recall that a subset of X is a base for G if its pointwise stabiliser is trivial. The base size of G, denoted b(G), is defined to be the minimal size of a base. This natural invariant has been intensively studied for many years, finding a wide range of applications. In this talk I will report on recent progress concerning a project initiated by Jan Saxl in the 1990s, which seeks to determine all the primitive groups with b(G) = 2. I will also outline some of the main applications and I will highlight one or two related problems.
This video was produced by the Isaac Newton Institute, as part of the workshop Simple groups, representations and applications, forming part of the programme Groups, representations and applications: new perspectives.
