Discrete Geometry and Combinatorics Seminar

Florian FrickCarnegie Mellon University
The Borsuk-Ulam theorem in combinatorics and geometry

Monday, October 17, 2022 - 2:30pm
Malott 206

Abstract: The classical Borsuk--Ulam theorem has numerous consequences across mathematics. It states that any continuous map from an n-sphere to Rn must identify antipodal points. I will present some new applications of this result, such as:

Codes in projective spaces through the Borsuk-Ulam theorem control structural results for zeros of raked trigonometric polynomials and more general maps.
For which pairs (d,n) does a continuous fibration of a region in Rn by unit d-spheres exist?
Generalizations of Lovász' lower bounds for chromatic numbers of graphs to obstructions for chromatic mixing.