I will give a sampling of examples illustrating how topological ideas arise in neuroscience. First, I'll tell you about some interesting neurons, such as place cells and grid cells, and the topology associated to their neural activity. I will also explain how convex neural codes capture additional features of the stimulus space, such as intrinsic dimension. Second, I'll explain how the statistics of persistent homology can be used to detect - or reject - geometric organization in neural activity data, using examples from hippocampus and olfaction.

Carina Curto received an A.B. in Physics from Harvard, and did her Ph.D. in Mathematics at Duke in algebraic geometry and string theory. She then spent her postdoctoral years at Rutgers and NYU, doing research in computational neuroscience and data analysis. In 2009 she became an assistant professor at the University of Nebraska-Lincoln, and in 2014 she moved to Penn State, where she is currently a professor in the Math department.