Zusammenfassung für den Vortrag am 20.06.2022 (14:00 Uhr)

Seminar on Nonlinear Algebra

Florian Frick (Carnegie Mellon University & FU Berlin)
The Borsuk–Ulam theorem, its generalizations, and applications

The Borsuk–Ulam theorem has found numerous applications across mathematical disciplines since its discovery in the 1930s. The theorem states that any continuous map from a d-sphere to d-space identifies a pair of antipodal points. I will show that this result remains relevant today and present new consequences. I will present two recent generalizations of the Borsuk–Ulam theorem, a colorful extension and a version for high-dimensional codomains, and explain some connections with packings of projective space among other topics.

This is joint work with Henry Adams, Johnathan Bush, and Zoe Wellner.