Bridging graph theory and network science
With the rise of data science, applications of network theory now arise in all shapes and forms; even in fields where they probably should not. Unfortunately, there is still a large gap between the foundations of graph theory and the simple application of “network thinking”. I have many projects which aim at closing this gap and unify the approaches from statistical physics, mathematics and computer science.
Epidemics on networks
The description of a propagating agent on a network describes multiple phenomena: epidemics, pollutants in food webs, viruses on the Internet, rumors in social groups and even the robustness of communication networks or nuclear fragmentation. My recent work on the subject has mainly been centered around four topics: mean-field descriptions on realistic topologies, co-evolutive dynamics (adaptive networks or competing processes), general stochastic description and exact solutions using bond percolation formalisms.
Complexity and criticality
Myriads of real complex systems (from works of art to biological systems) share common, universal, features of organization. Many of the models proposed to explain the emergence of such properties (e.g. self-organized criticality and other critical processes) also share common features or rules. I am interested in finding these “hidden” laws of organization in the hope of gaining further insights on the necessary ingredients of complexity.