Title: Chromatic number of ball packings and the Borsuk conjecture
Abstract: A ball packing is a set of balls with disjoint interiors. I
will talk about a surprisingly recent problem that deserves more
attention: What is the maximum chromatic number for the tangency graph
of a ball packing in dimension d? The current upper bound is
exponential (w.r.t. the dimension), while the lower bound is linear.
When the balls are of the same radius, the problem is the "opposite" of
the Borsuk conjecture. Recent progress on the Borsuk conjecture lead to
a slight improvement on the lower bound, and the approach makes use of
strongly regular graphs.