Symplectic Embeddings of Rational Homology Balls into Projective Space

I will discuss how to build small symplectic caps for contact manifolds as a step in building small closed symplectic 4-manifolds. As an application of the construction, I will give explicit handlebody descriptions of symplectic embeddings of rational homology balls into CP^2. This is joint work with Hyunki Min, Lisa Piccirillo, and Agniva Roy.