In this internet era where 2.5 quintillion bytes of data are created per day, the development of

techniques for efficiently aggregating this dizzying amount of data has become a matter of utmost

importance. The relevance of the formalization of this simple notion of aggregation can be

quantified by countless papers, special issues, edited volumes, monographs, conferences, summer

schools, etc. Indeed, there exists a whole community centred on the study of aggregation

processes. However, although it constitutes an impressive body of mathematical knowledge, most

theoretically-oriented studies are confined to the aggregation of real numbers or, in more exotic

cases, to other ordered structures, such as intervals or ordinal linguistic scales. Shamefully, the

aggregation of non-ordered structures, such as graphs, strings and ranking data, is mostly

addressed by practitioners. One could say that, while the practical framework is full of "ad hoc"

methods, the theoretical framework is embarrassingly narrow. Both theory and practice do not

hitherto converge. This divergence is mainly motivated by two factors: 1) the difficulty of fully

understanding some black-box-esque practical aggregation techniques 2) the computational

challenge that applying some complex theoretical aggregation techniques implies. In this

postdoctoral proposal, we will address the development of a new theory of aggregation that

finally brings theory and practice together.