# PhD Confirmation Seminar

## 4:30 pm

## Monday, 27^{th} Nov 2017

**VG31, Mathematics Building**

# Theo Bendit

(The University of Newcastle)
*Chebyshev Sets on the Sphere*

The Chebyshev conjecture is a 59-year-old open problem in the fields of analysis, optimisation, and approximation theory, positing that Chebyshev subsets of a Hilbert space must be convex. Inspired by the work of Asplund, Ficken and Klee, we investigate an equivalent formulation of this conjecture involving Chebyshev subsets of the unit sphere. We show that such sets have superior structure and use the Radon-Nikodym Property to extract some local structural results about such sets.