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Derived categories, Gromov--Witten invariants, and mirror symmetry have been actively studied in the last two decades and proved to be very important in both geometry and theoretical physics. Our main motivation to organize this conference is to focus on the applications of these new ideas to birational geometry. Our hope is that by bringing together top specialists from all over the world, we will give an account of the achievements, as well as an outline of what are the next challenges. While our original motivation is very specific, we are expecting to have a wide variety of topics, such as homological mirror symmetry, non-commutative Hodge structures, Gromov--Witten invariants, etc. We will try to keep the number of talks to a minimum, leaving plenty of room for free discussions.