This webinar features presentations from SueYeon Chung (New York University) and Srinivas Turaga (HHMI Janelia Research Campus) on theoretical and computational approaches to sensory cognition. Chung introduced a “neural manifold” framework to capture how high-dimensional neural activity is structured into meaningful manifolds reflecting object representations. She demonstrated that manifold geometry—shaped by radius, dimensionality, and correlations—directly governs a population’s capacity for classifying or separating stimuli under nuisance variations. Applying these ideas as a data analysis tool, she showed how measuring object-manifold geometry can explain transformations along the ventral visual stream and suggested that manifold principles also yield better self-supervised neural network models resembling mammalian visual cortex. Turaga described simulating the entire fruit fly visual pathway using its connectome, modeling 64 key cell types in the optic lobe. His team’s systematic approach—combining sparse connectivity from electron microscopy with simple dynamical parameters—recapitulated known motion-selective responses and produced novel testable predictions. Together, these studies underscore the power of combining connectomic detail, task objectives, and geometric theories to unravel neural computations bridging from stimuli to cognitive functions.