We describe a list of open problems in random matrix theory and the theory ofintegrable systems that was presented at the conference Asymptotics inIntegrable Systems, Random Matrices and Random Processes and Universality,Centre de Recherches Mathematiques, Montreal, June 7-11, 2015. We also describeprogress that has been made on problems in an earlier list presented by theauthor on the occasion of his 60th birthday in 2005 (see [Deift P., Contemp.Math., Vol. 458, Amer. Math. Soc., Providence, RI, 2008, 419-430,arXiv:0712.0849]).
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