A mathematical approach to some problems in neurobiology

I will discuss some questions of interest in neuroscience, seen through the lens of mathematics. No prior knowledge of neuroscience is needed for this talk. Two of the most basic visual capabilities of primates are orientation selectivity, i.e., the ability of neurons to discern orientations of edges, and direction selectivity (DS), their ability to detect the direction of motion. Both properties are enjoyed by neurons in the primary visual cortex (V1), where visual information enters the cerebral cortex, but not by cells that provide input to V1. I wanted to understand the biological origins of these visual functions, especially that of DS, which had remained a mystery for half a century. Building on well known results of Hubel and Wiesel, I will propose ideas that are grounded in biology, tested in large-scale dynamical models of the visual cortex, and shown to be consistent with experimental data. Most of all I would like to share the little bits of mathematical insight that contributed to these results in visual neuroscience.