Lipschitz extension problems have received wide research attention over
the years. Many results are known for domain and target spaces with a
linear structure or with upper and lower curvature bounds. More
recently, Lipschitz extension problems have been studied when the target
space is a so-called Carnot-Caratheodory space. Carnot-Caratheodory
spaces appear most prominently in the field of Analysis on metric
spaces; particular examples are given by the Heisenberg groups. The aim
of this talk is to give an introduction for non-specialists of the
Lipschitz extension problem and describe in more detail recent results
for Carnot-Caratheodory space targets. In parts based on collaborations
with Severine Rigot and Robert Young.

[Invited by Dr. Patrick Ghanaat]