# Lecture by Florian Frick (Carnegie Mellon University): New applications of the Borsuk--Ulam theorem

The classical Borsuk--Ulam theorem states that any continuous map from the d-sphere to d-space identifies two antipodal points. Over the last 90 years numerous applications of this result across mathematics have been found. I will survey some recent progress, such as results about the structure of zeros of trigonometric polynomials, which are related to convexity properties of circle actions on Euclidean space, a proof of a 1971 conjecture that any closed spatial curve inscribes a parallelogram, and finding well-behaved smooth functions to the unit circle in any closed finite codimension subspace of square-intergrable complex functions.

### Time & Location

Jan 18, 2021 | 02:15 PM

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