SPECIAL MATHEMATICS COLLOQUIUM
Speaker: Chad Giusti
Abstract. The study of neural networks, both biological and artificial, is confounded by the intrinsically nonlinear nature of the elements of the system at any scale; for example, the electrophysiological response of individual neurons to stimuli or the voxel-wise BOLD signal as a correlate for electrical activity in fMRI. In trying to understand the organization and activity of such systems, it is useful to begin by asking what observations we can trust -- that is, what properties of our data are invariant under such confounds. The answer to this question leads us naturally to classical theorems from combinatorial topology and modern computational tools from applied algebraic topology. Here, we will touch on several lines of work motivated by these ideas, including theoretical results on the coding properties of neural networks and the analysis of neural recordings in human and animal models.