Abstract 

In this talk, we will present the main representation results of mathematical morphology for set operators and particularise them for the important class of translation-invariant and locally defined set operators. Then, we will show how these results are extended to operators in general complete lattices and how they can be leveraged to design operators with desired properties. Finally, we will discuss how these results can be applied to develop data-driven operator learning methods that consider an overparametrisation of the operator class to enhance the efficiency of learning algorithms, but that have an associated algebraic representation that allows the deduction of the mathematical properties of the learned operator.