UBC Discrete Math Seminar: Alexander Ruys de Perez

A neural code C on n neurons is a collection of subsets of the set of integers {1,2,...,n}. Usually, C is paired with a collection of n open subsets of some Euclidean space, with C encoding how those open sets intersect. A central problem concerning neural codes is determining convexity; that is, if the code can encode the intersections of n convex open subsets. In this talk, I will generalize an example of Lienkaemper, Shiu, and Woodstock (2017) into a new criterion for nonconvexity called a 'wheel'. I will show why it forbids convexity, explain how one can find it combinatorially, and provide examples of previously unclassified codes that we now know to be nonconvex due to containing a wheel.