In their paper "Symplectic packings and algebraic geometry", McDuff and Polterovich showed that the existence of a symplectic embedding of a disjoint union of balls into a symplectic manifold $M$ of the same dimension is equivalent to the existence of a symplectic form on the complex blow-up $\tilde{M}$ of $M$ which lies in a certain cohomological class and satisfies a certain additional property.   One can consider symplectic embeddings which additionally respect some complex structure on $M$. A symplectic embedding is called Kähler-type if it is holomorphic with respect to some integrable complex structure compatible with the symplectic form. Recently Entov and Verbitsky studied properties of the space of Kähler-type embeddings and proved a similar criterion for the existence of such embeddings using techniques of complex geometry.   In my talk I will present generalizations of these results to the case of symplectic and Kähler-type embeddings of disjoint unions of ellipsoids, and will apply them to study such embeddings into specific target manifolds. Advisor: Prof. Michael Entov