Title: Vietoris—Rips complexes, projective codes, and zeros of odd maps
Speaker: Johnathan Bush (University of Florida)
Speaker's URL: https://people.clas.ufl.edu/bush-j/
Abstract: I will describe relationships between the following three problem areas: (i) understanding the topology of Vietoris—Rips complexes of spheres, (ii) finding large collections of nearly orthogonal vectors in euclidean spaces called projective codes, and (iii) bounding the diameter of zero sets of odd maps from spheres to euclidean spaces. We will use these relationships to prove a generalization of the Borsuk—Ulam theorem in which the dimension of the codomain of a map of a sphere may exceed the dimension of the sphere. In turn, this generalized Borsuk—Ulam theorem will allow us to prove generalized versions of the Ham Sandwich theorem and the Lyusternik—Shnirel'man covering theorem. Time permitting, we will also use these results to sketch a new proof of a result of Simonyi and Tardos on topological lower bounds for the circular chromatic number of a graph.
URL associated with Seminar: https://tgda.osu.edu/activities/tdga-seminar/
Zoom: https://osu.zoom.us/j/93628189417?pwd=a0l3aU5OM3Z6U09lZFllYlJ0Tis0QT09
