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Gravitational radiation promises to teach us many new
things about the universe and the world around us, but all attempts to observe
gravitational waves have so far been unsuccessful.  I will discuss some of the challenges we need
to overcome in our quest to detect this elusive form of energy, and how
tackling these challenges is opening new windows on fundamental physics.  I will show, specifically, how novel data
analysis strategies have been used to combat detector noise in searches for
gravitational waves from cosmic strings, and how the search for the signatures
of neutron star collisions has created new techniques for modelling the mergers
of compact objects.

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