Overview

Recent advances in neuroscience reveal that neural activity often exhibits striking geometric structure across sensory, cognitive, and motor systems. For instance, low-dimensional neural activity manifolds encode behavioral and cognitive variables in many brain regions, and these manifolds can vary less across time, individuals, and species than single neuron activity. These findings suggest that geometry is fundamental to neural computation and may provide a unifying perspective on how neural systems represent information, perform computations, and support behavior.

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This workshop will bring together experimentalists, theorists, and mathematicians to identify geometric principles underlying neural computation, highlight open mathematical challenges, and foster collaborations at the interface of neuroscience and geometry. Neuroscience topics will include representational geometry in neural population activity, the structure and function of neural manifolds, the geometry of parameter landscapes underlying neural computation and learning, and geometric and topological approaches to high-dimensional neural data. The workshop aims to both highlight existing mathematical ideas in neuroscience and identify new mathematical questions inspired by neural systems. Relevant areas of mathematics include differential geometry, topology, dynamical systems, optimization, and information geometry. The program will include invited talks, focused discussions, and opportunities for informal exchange aimed at developing a common language for describing neural systems in geometric terms.