Pure Maths Colloquium: Matthew Brookes

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

Where: Purdie Theatre C
When: Feb 3 2022 @ 16.00
Video: Link (internal)
Speaker: Matthew Brookes University of St Andrews
Title: Congruence relations for inverse semigroups

Inverse semigroups are a natural generalisation of groups, with actions of inverse semigroups modelling partial automorphisms of algebraic structures. One and two sided congruences take up the role for semigroups that subgroups and normal subgroups take on for groups. The set of congruences on any semigroup is partially ordered by inclusion, and this ordering forms a complete lattice. In this talk I will discuss how congruence relations on inverse semigroups may be described in terms of pairs consisting of a subsemigroup and a congruence on the semilattice of idempotents.