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A resonance is a concept of great importance in various
physical theories, from classical wave propagation to high-energy
particle scattering.  But resonances are also fascinating quantities
in a purely mathematical context.  For example, the Prime Number
Theorem could be seen as a result on the distribution of resonances
associated to a particular surface.  This talk will explain in very basic 
terms what a resonance is and then give some examples to illustrate
the interesting connections between resonances and various topics 
in geometry and number theory.
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