BCFT: from the boundary to the bulk

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The study of boundary conditions in rational conformal field theories is not only physically important. It also reveals a lot on the structure of the theory ``in the bulk''. The same graphs classify both the torus and the cylinder partition functions and provide data on their hidden ``quantum symmetry''. The Ocneanu triangular cells -- the 3j-symbols of these symmetries, admit various interpretations and make a link between different problems.
Talk presented at TMR-conference "Nonperturbative Quantum Effects 2000", 7 pages, LATEX with JHEP proceedings style

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