On Wilson's existence theorem and the monoid of continuous maps on block designs

In 1974 Rick Wilson proved one of the most important theorems on combinatorial structures in the 20th century by showing that the easy necessary conditions on the parameters of a block design are eventually sufficient. The proof involves morphisms between block designs whose fibers allow for recursive constructions. The self-maps of a design form a monoid that are a fundamental part of the theory of designs. The algebraic properties of this monoid have not been explored up to now and the purpose of this talk is to do just that. We give a beautiful connection between semigroups, groups designs and incidence geometry.

No background in either design theory or semigroup theory is required for the talk. This is joint work with John Rhodes and Pedro Silva.