Towards a mathematical understanding of neural mechanisms of visionI will discuss some recent work on two of the most crucial visual capabilities of the Macaque monkey, whose visual system is very similar to that of humans. The two capabilities are orientation selectivity (OS), 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), but not by cells that provide input to V1. Two scientific questions, therefore, are biological origins of these visual capabilities. For OS, the hypothesis of Hubel and Wiesel half a century ago offered important clues. No plausible explanation of DS for monkey had been found. After a brief review of relevant facts, I will propose a theory that is grounded in biology and tested in large-scale models the outputs of which compare well with data. Most of all I would like to convey the mathematical thinking that contributed to these results in visual neuroscience.
Lai-Sang Young is a Professor of Mathematics at the Courant Institute and Henry and Lucy Moses Professor of Science at NYU. She is currently also a Distinguished Visiting Professor at the Institute for Advanced Study, Princeton. Young started her career in pure Mathematics, specializing in Dynamical Systems. She is best known for her work on chaos, for which she was awarded the Jurgen Moser Prize for distinguished contributions to nonlinear science. In the last 20 years she has expanded her research to include applications of dynamical systems ideas to Mathematical Physics and to Computational Neuroscience. Young has delivered plenary lectures in the International Congress of Mathematicians and the International Congress on Mathematical Physics. She is a member of the US National Academy of Sciences and a member of the American Academy of Arts and Sciences.