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Monday, May 5, 2014

**Abstract:** We prove that every symplectic toric orbifold is a "centered" symplectic reduction of a Cartesian product of weighted projective spaces. Reduction is centered if the level set contains central Lagrangian torus fiber of the product of weighted projective spaces. In that case one can deduce certain information about non-displaceable sets or existence of quasimorphisms. For example, a theorem of Abreu and Macarini shows that if the level set of the reduction passes through a non-displaceable set then the image of this set in the reduced space is also non-displaceable. Using this theorem and our result we reprove that every symplectic toric orbifold contains a non-displaceable fiber and identify this fiber. Joint work with Aleksandra Marinkovic.