Theoretical issues in J/psi suppression

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Two decades ago Matsui and Satz suggested that Debye screening in the quark-gluon plasma would result in J/psi suppression in heavy ion collisions. Much has happened in the subsequent years, and the picture of quark-gluon plasma at present is rapidly evolving - what does it imply for the J/psi suppression? What are the recent RHIC and SPS results trying to tell us? What else has to be done? This talk is an attempt to address these questions.
8 pages, 6 figures, invited plenary talk at Quark Matter -2006, Shanghai, China, November 14-20, 2006

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