Lethbridge Number Theory and Combinatorics Seminar: Roberto Budzinski

Understanding how network structure gives rise to spatiotemporal dynamics and computation is a central challenge in computational neuroscience and artificial intelligence. Despite increasingly detailed connectomic data in neuroscience and large-scale datasets in machine learning, establishing principled links between connectivity, dynamics, and function in nonlinear neural systems remains difficult. In this talk, I will present a mathematical framework that directly relates network architecture to emergent dynamical patterns and computational capabilities in analytically tractable models. Our approach focuses on networks of coupled oscillators, which are widely used to model interacting neural populations and have recently gained interest as computational substrates in artificial neural networks. With this approach, we can show how key structural features of these networks — including connectivity patterns and transmission delays — determine the emergence and stability of spatiotemporal activity, enabling analytical predictions of collective phenomena such as traveling waves. When applied to empirically derived brain networks, the framework provides a rigorous connection between large-scale anatomy, distance-dependent delays, and wave dynamics observed at mesoscopic and whole-brain scales. Building on these results, we introduce a new class of neural networks that leverage structured spatiotemporal dynamics for computation while remaining exactly solvable. Together, these results outline a general strategy for linking network structure, emergent dynamics, and computation, with implications for understanding neural activity and for developing interpretable dynamical models for neural computation.