Florian Frick (6/4/21): Rips complexes, projective codes, and zeros of odd maps

We will discuss a relation between the topology of Rips complexes (or their metric versions), the size of codes in projective spaces, and structural results for the zero set of odd maps from spheres to Euclidean space. On the one hand, this provides a new topological approach to problems in discrete geometry. On the other hand, these results give another piece of evidence that understanding the topology of Rips complexes of spheres is difficult. This is joint work with Henry Adams and Johnathan Bush.