(updated February 13, 2019)

Monday, 13 May, morning (9.30-12.30)
The New Science of Networks (Latora): Networks constitute the backbone of complex systems, from the human brain to computer communication, transport infrastructures to online social systems and metabolic reactions to financial markets. Characterising their structure improves our understanding of the physical, biological, economic and social phenomena that shape our world. As a result, complex networks have become an essential ingredient in the background of any scientist. In my first lecture I will present an overview of the new theory and methods of network science, of the main results found, and of some of the still open challenges.

Monday, 13 May, afternoon (14.30-17.30)
Network Geometry (Petri): Simplicial complexes and complex systems, a general introduction. Structural properties of simplicial complexes; local and global observables, basics of homology. Models of simplicial complexes: random null models, configuration and exponential models, growing models. Complex network geometry and manifolds; dynamics of and on simplicial complexes: activity driven model, percolation, epidemic spreading and synchronization.

Tuesday, 14 May, morning (9.30-12.30)
Complex Networks with Many Layers (Latora): The constituents of a wide variety of real-world complex systems interact with each other in complicated patterns that can encompass multiple types of relationships and can also change in time. In my second lecture I will concentrate on the structure and dynamics of multi-layer networks, discussing cases where the presence of many layers gives rise to the emergence of novel behaviours, otherwise unobserved in single-layer networks. Topics covered: From complex systems to multilayer networks; Structural properties of networks with many layers; Modelling the growth of a multiplex network; Reducibility of multilayer networks; Dynamical properties of multilayer networks.

Tuesday, 14 May, afternoon 
no lectures

Wednesday, 15 May, morning (9.30-12.30)
Topological Data Analysis (Petri): Topological simplification (Mapper), optimization and automatic parameter selection; statistical validation and applications to social and biological systems; introduction to persistent homology, robustness and localization, distances between homological summaries; applications to the structure of networks, embeddings of dynamical processes, brain imaging data and neural networks.

Wednesday, 15 May, afternoon (14.30-17.30)
short talks by students (see page Application)

Wednesday, 15 May, evening (20.00)
social dinner

Thursday, 16 May, morning (9.30-12.30)
Machine Learning and Networks (Eliassi-Rad): Supervised and semi-supervised learning in networks: relational dependencycollective classification, and network sampling; unsupervised learning in networks: community discoveryrole discoverygraph representation learning, and anomaly detection.

Thursday, 16 May, afternoon
no lectures

Friday, 17 May, morning (9.30-12.30)
Ecological Networks (Kéfi): Networks provide powerful tools to visualize and quantify the complexity of ecological systems. In this lecture, I’ll present some of the broad questions that have been addressed with networks in ecology. I’ll give an overview of recent (and less recent) studies on the structural regularities of ecological networks, and what we know about the links between these structural properties and ecological network dynamics, and in particular their resilience to perturbations.

Friday, 17 May, afternoon (14.30-17.30)
Collective Sensing and Decision-Making in Animal Groups: From Fish Schools to Primate Societies (Couzin): Understanding how social influence spreads in networks is a key challenge in the study of collective behaviour. I will demonstrate new imaging and virtual reality technology that allows us to reconstruct (automatically) the dynamic, time-varying sensory networks by which social influence propagates in groups. I will show how this allows us to identify, for any instant in time, the most socially-influential individuals, and to predict the magnitude of complex behavioral cascades within groups before they actually occur. I will address how structural properties of real social networks impact the coupling between spatial and information dynamics, and will reveal the importance of uninformed nodes in facilitating fast and effective collective decision-making.