Algebraic Structures on Symplectic Homology and Their Applications

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The subject of this project is symplectic homology, an invariant of symplectic manifolds with contact type boundary. This proposal has two goals. The first one is to enhance this theory by introducing additional algebraic structures. The second goal is to apply these new structures to specific problems in symplectic topology: Lagrangian embeddings and immersions, contact embeddings, topology of symplectic fillings, and relations to the theory of singularities.