ALGB Seminar: Sam Mattheus
Title: Non-commutative algebras from finite geometry
Abstract: Highly symmetrical combinatorial objects lead to algebraic structures, that is a fact. The simplest instance of this fact is the existence of the symmetry group of such an object. This is how groups are often introduced to students. However, depending on the objects, we can sometimes build a richer algebraic structure associated to them. For example, association schemes and their non-commutative generalizations called coherent configurations are two types of algebras are two of those. We will introduce these algebras and show how they can be used to obtain results in finite geometry.