Topology as a Tool for Comparing Population Activity and Studying Learning

Explore how topological methods can be applied to understand neural computation and learning in this mathematical neuroscience lecture. Learn about the connection between receptive fields and neural manifolds, discovering how viewing individual fields as open sets naturally leads to topological analysis of brain structure. Survey the fundamental topological concepts underlying this mathematical framework, then examine recent research on how topologically structured information flows across neural populations. Investigate methods for studying the learning of these structures in spiking neural networks, with applications to understanding how the brain processes and learns complex patterns. Gain insights into this interdisciplinary approach that bridges mathematics and neuroscience without requiring prior knowledge of topology.