Guillaume’s research interests lie at the intersection of mathematics and neuroscience. More specifically, his work aims at developing and applying mathematical tools to approach problems of driven neural networks. Guided by this theme, he works on projects falling in two main categories. The first relates to synchrony, or lack thereof, in neural populations receiving a common input. This is intimately linked to studies of neural pathologies such as Parkinson’s disease and their treatments via neuroprosthetics. Here, synchronous dynamics within certain neural nuclei disrupt normal brain functions and electrical stimulation can restore them. How do these networks synchronize? How can we break this synchrony with global inputs? He uses a variety of tools such as geometric perturbation theory, discrete dynamical systems and numerical simulations to approach such problems.
The second category is motivated by neural coding, or the ability of neural networks to encode information from a stimulus that perturbs its dynamics. He investigates the reliability of excitable neural networks, driven by a given input signal. Reliability can be described as the ability of a dynamical system to reproduce the same output, given a single stimulus, on many trials where initial conditions change. Moreover, he wishes to address questions on information carrying capacities of such networks and the role of reliable behavior in this context: When are excitable neural networks reliable? What are the implications for possible encoding schemes given a reliable (or unreliable) network? Here, he uses a blend of bifurcation theory, numerical simulations and information theoretic tools to attack these questions.
Before he joined the applied mathematics department at UW, in 2008, he completed an undergraduate degree and a masters degree in mathematics at the University of Ottawa, Canada. He specialized in the study of dynamical systems theory. He then got interested in applying my acquired knowledge to one of the most complex and exciting system found in nature: the brain. This is the main reason why I moved to Seattle and joined the computational neuroscience research community at UW. He also admits that apart from its academic merits, he was attracted to the Seattle area for its proximity to an amazing vertical playground. Indeed, when he is not working, you can almost surely find him in the mountains, where he gets my fix of rock and alpine climbing.