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A Galois connection for operations and relations

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If you have a question about this talk, please contact Nathanael Alcock.

Galois connections are a relatively simple type of duality that are plentiful in maths and computer science. In this talk, I’ll give some background on these, their history and generalisations, before focusing on an example of particular importance to logic and theoretical computer science: the Pol-Inv connection. This simple construction relates finitary operations on a set to finitary relations on the same set in a way that allows you to turn questions about algebraic structure into questions about logical/relational structure, and vice versa. I’ll outline some nice features and recent applications of this connection, including to the (recently resolved) CSP Dichotomy Conjecture.

This talk is part of the Logic & Semantics for Dummies series.

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