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Abstract: I will show how the idea of multiple equilibria was emerging in various fields in the seventies. However, the first realization of this idea in a mathematical physics setting was obtained in the theory of spin glasses. I will show how in an equilibrium setting the states have an ultrametric structure and therefore they are leaves of the universal tree of states discussed by Ruelle and by Bolthausen and Sznitman.
A brief discussion will be presented on open problems.