Neural fields equations, from Wilson-Cowan to neural engineering

The modeling of collective behavior within a neuronal population, initiated by the pioneering work of Wilson and Cowan, has been a great source of inspiration in the computational neuroscience community. Indeed, the focus on the overall neuronal activity of a brain structure, rather than on the detailed evolution of the electric response of single neurons, allows to adequately model a vast range of brain functions and opens the door to a mathematical understanding of the processes involved. Moreover, the spatio-temporal version of this model, known as neural fields, allows one to consider spatial heterogeneity within a cerebral structure, at the price of more demanding analysis tools. Neural fields have been used in the investigation of a wide range of applications, including the modeling of sensory cortices, cognition, human-robot interaction, self-organizing maps, visual hallucinations, and deep brain stimulation. Despite great advances made on the mathematical understanding of these models, research on these models still progresses in several directions, including: - finer analysis of their behavior in a non-local regime - parameter identification based on experimental data - controllability analysis, e.g., to understand how to affect the dynamics via external stimulation - observability analysis, e.g., to determine the optimal sensor-placement strategy allowing to reconstruct the overall dynamics The aim of this workshop is to gather researchers from different fields (neuroscience, physics, mathematics, control engineering, computer science) to discuss the most recent advances on Wilson-Cowan and neural fields models and instill new collaboration opportunities on this topic.