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The main focus of this talk will concern the algebraic singularities that
can be realized by a symplectic curve of degree k in CP^2. I will explain on
one hand a strong relation between these singularities and symplectic
embeddings of specific domains. On the other, I will explain a flexibility
property at the level of symplectic embeddings of these domains in CP^2
(mainly due to McDuff). As a result, I will describe a flexibility property
of the singularities of a symplectic (or pseudo-holomorphic) curve.
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