I face two basic tasks: to create feasible and contrastable explanations for the complex reality we observe, and to make sense of an unprecedented wealth of empirical data available thanks to the current explosion in computing power. Accordingly, I organize my lines of research in two big entangled blocs to be developed simultaneously.

Development of Theoretical and Mathematical Tools: I will focus on two main topics. i) The connection between complex networks and hidden metric spaces. We can define distances (similarities) between all pairs of nodes to develop a true cartography of real complex networks. The discovery of hidden metric spaces and their understanding has become a major research area within complex networks science. ii) The characterization of the multilevel nature of complex networks. We need to understand the combined role of spatial distance, time, and interlayer interactions on the dynamics of processes running on multiplex networks and on the emergence of collective phenomena.

Applications to Real Networks: I will study systems in three different domains: biology, economy, and socio-technology. i) Study of disease vs healthy cell phenotypes, with a focus on cancer metabolism. In the long term, we aim at producing a whole-cell functional network integrating genome, proteome, and metabolism to mimic observed phenotypes and to predict cellular responses. ii) The gravity theory of trade flows is directly related with the connection probability we use in our hidden metric space models. We plan to map the world trade web according not only to geographic location but to actual aggregated barriers to international trade in the world. iii) Socio-technological networks stand as an unexpected outlook for observing real social processes. We can define an ICT mediated social distance encoding people's social attributes and technological aspects of ICT, which may help to design efficient and scalable information transmission protocols.