Mathematics Department
Colloquium
Friday, October 25, 2013, 4:00-5:00 p.m.
Room 2305 Centennial Hall
Kissing, Coding, Bounding, and Semi-Definite Programming
Edward Kim
University of Wisconsin-La Crosse
Abstract: In this talk, we will describe a particular problem which was the subject
of debate between the mathematicians Isaac Newton and David Gregory which
was finally settled in 1953 by Schütte and van der Waerden. The debate concerned
the number of spheres which could tangentially “kiss” another sphere, which is an
example of a question in coding theory. In this talk, we will describe modern
solutions to the kissing sphere problem for dimension 𝑛 = 3, describe known
results for the (𝑛 − 1)-sphere 𝑆 !!! = 𝑥 𝜖 ℝ! ∣ !!!! 𝑥!! = 1 , and discuss a
variant of the problem for hemispheres. The problems we will discuss are very
interesting because of its multidisciplinary nature: though the results rely on graph
theory, discrete geometry, convex optimization duality, harmonic analysis, and
representation theory, we will be able to summarize the tools we need without
introducing many technicalities.