*Set covering problems: from combinatorial geometry to the geometry of
numbers*

Abstract

In our talk, we will speak about two, apparently quite different, types
of problems. On the one hand, we shall discuss some classical questions
of combinatorial geometry such as Borsuk's partition problem and
Nelson--Hadwiger's problem on coloring metric spaces. On the other
hand, we shall treat of a problem in the geometry of numbers. A bridge
between the two types of problems will be built by one more problem
in pure combinatorics --- the set covering problem.