  We prove that the presence or absence of corners is spectrally determined in
the following sense: any simply connected domain with piecewise smooth
Lipschitz boundary cannot be isospectral to any connected domain, of any genus,
which has smooth boundary. Moreover, we prove that amongst all domains with
Lipschitz, piecewise smooth boundary and fixed genus, the presence or absence
of corners is uniquely determined by the spectrum. This means that corners are
an elementary geometric spectral invariant; one can hear corners.
