Speaker:  Florian Frick, Carnegie Mellon University
Title: The Borsuk-Ulam theorem in combinatorics and geometry
Time: 2:30 PM, Monday, October 17, 2022
Place:  Malott 206

Abstract: The classical Borsuk--Ulam theorem has numerous consequences across mathematics. It states that any continuous map from an $n$-sphere to $\mathbb{R}^n$ 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 $\mathbb{R}^n$ by unit $d$-spheres exist?
• Generalizations of Lovász' lower bounds for chromatic numbers of graphs to obstructions for chromatic mixing.