Median spaces are metric spaces in which given any 3 points,
there exists a unique median point, that is a point lying on 3 geodesics
between those 3 points. We will explain how median spaces are a natural
generalisation of CAT(0) cube complexes, how one characterizes property (T)
and the Haagerup property using median spaces and how the fundamental
group of a 3-dimensional manifold acts on a median space. This is joint
work with C. Drutu and F. Haglund.

Lecture #12570

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