In this talk I will review some of the contributions of our group on the topic. I will start with the most basic diffusion processes, and finish with the more complex combination of different processes on different layers. Special emphasis will be placed on the spectral aspects of the mathematical description. Examples are taken from Physcis, but also from Social Sciences, Biology or Neuroscience.
I have carried out a research work of relevance in the subject of science of complex systems. In particular, since its inception, in 1998, I have devoted many efforts to the field of complex networks. Throughout this period, I have published in some of the most prestigious journals in the field of complex systems giving rise to a very good record of citations. Some of these publications have become seminal papers in the field, for instance, my contributions to the synchronization in complex networks, my works on community detection, and my vision of multiplex networks. Fortunately, this activity has been possible thanks to numerous funded projects, including a continuous source of funding from the Spanish and Catalan funding agencies.
This line of continuous efforts has led me to constitute a large group (among researchers from the University of Barcelona and the Rovira i Virgili University) of international reference in this field, since in recent years we have obtained alternative sources of funding not expected in normal conditions, such as European projects and contracts with companies, and organizing the most important conferences in the field.
Throughout my career, I have had the privilege of supervising a large group of young researchers, as director of doctoral thesis. In this sense, there remains the satisfaction of seeing that most of them have undertaken research careers, both in academic and in business settings, highlighting the relevance of the science of complex networks as applied to other disciplines and to businesses. At the same time, it has been an immense pleasure to have collaborated with outstanding scientists from many diverse disciplines in the past.