Mathematical models of the human brain in health and disease

Understanding how the mind, encompassing all of our thoughts, feelings, behaviours, emotions, and experiences, emerges from the physical substrate of the brain is one of the major scientific challenges of our time. A deep understanding of this problem must be achieved through mathematical models. Fortunately, the recent availability of experimental data quantifying diverse aspects of brain structure and function has made it possible to develop biophysically constrained mathematical models of diverse aspects of brain development, function, and disease. Several projects are on offer to students that will address major questions such as: * how does the anatomy of the brain constrain its spatiotemporal dynamics? * how do disease processes affecting the brain evolve through time and can we predict patterns of brain change in individual patients? * what are the key physical and physiological constraints that shape brain organization? These projects will be suitable for students interested in graph theoretical models of physical growth processes, differential geometry, complexity, and dynamical systems theory.