Recorded 16 February 2024. Smita Krishaswamy of Yale University presents "Inferring and Characterizing Neuronal Connectivity and dynamics with deep geometry and topology" at IPAM's Mathematical Approaches for Connectome Analysis Workshop. Abstract: In the critical stages of embryonic development, neurons form intricate networks by extending axons to establish contacts with neighboring cells and identifying synaptic partners. The rules that dictate these neural connections remain largely elusive. In this talk, I’ll describe novel methods based on geometry and topology to decode these organizational rules using data derived from the C. elegans nerve ring. First, I’ll introduce diffusion condensation, a novel technique to quantify and visualize neuroanatomical architecture across multiple spatial scales via a time-inhomogeneous diffusion process. Next, I’ll delve into topological data analysis of the nerve ring, using persistent homology to identify and track changes in clusters and feedback loops in neural circuits over development. Together, these approaches elucidate how the developing nervous system's architecture adapts to allometric growth through time. In general, our analysis supports the hypothesis that persistent area contacts between neurons predate the formation of stable chemical synapses. I will also preview a deep learning technique we have developed called RITINI (Regulatory Temporal Interaction Inference) that allows for inference of neuronal networks and circuits using a graph ODE that is trained to predict neural signal dynamics. This technique offers the possibility of using data-driven approaches to infer connectivity before the topological analysis. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/mathematical-approaches-for-connectome-analysis/?tab=overview