Course "Unification and Duality: a fruitful interaction" - Talk 1: Introduction. Unification module theories

This is a series of talks on the interaction between apparently unrelated topics – unification modulo equational theories, and topological dualities for varieties of algebras. I will cover the basics of unification theory, and will give a cursory introduction to duality theory. I will then advance the claim that the latter is a useful tool in the context of the former, and support it by a detailed analysis of a few case studies. I will conclude the series with a discussion of notable open problems in the field. The level of the exposition will be aimed at an audience of colleagues.