Topological and Geometric Methods in Neuroscience

Learn to apply topological and geometric methods to modern neuroscience challenges in this comprehensive tutorial that bridges mathematical frameworks with real-world neural data analysis. Begin with an introduction to theoretical neuroscience, exploring typical neuroscientific datasets and understanding which questions current methods can address versus those that remain challenging. Discover how recent technological advances have revolutionized our view of neural circuits, from single-neuron dynamics to complete connectome mapping, while grappling with the profound analytical challenges this data explosion presents. Master key geometric and topological approaches including directed graph modeling for neuronal networks and persistent homology with Betti curves for large-scale neural recordings analysis. Explore how these mathematical tools can reconcile experimental findings with theoretical models and potentially unify different approaches to understanding neural circuits and dynamics. Designed for participants with minimal topology and graph theory background, gain practical experience applying these methods to real-world datasets, examining how topological and geometric frameworks address fundamental questions about brain function and neural circuit behavior.