In quantum or electromagnetic scattering theory resonances correspond to states which have a certain rest energy and a rate of decay (given by the real and imaginary parts of a complex resonance, respectively). I will survey results is scattering theory by trapping and non-trapping perturbations and present recent advances concerning lower bound on quantum decay rates and on fractal Weyl laws. I will also present some recent theoretical and experimental results related to these topics. The talk is based on joint work with S Nonnenmacher and J Sj\"ostrand.
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