My main research interests lie
in geometric group theory, low-dimensional topology, and the
study of metric spaces of non-positive curvature, as you will
see from the summary of my work given in the following items.
"I may say that this is the greatest factor -- the way in which the expedition is equipped --
the way in which every difficulty is foreseen, and precautions taken for meeting or avoiding
it. Victory awaits him who has everything in order -- luck, people call it. Defeat is certain
for him who has neglected to take the necessary precautions in time; this is called bad luck."