Abstract: n this talk, we will give an introduction to $RO(G)$-graded cohomology, which, in a certain sense, extends Bredon cohomology.

Abstract: In this presentation, we investigate the embeddings of five disjoint closed balls into the complex projective plane $\mathbb{C}P^2$. In 1985, Gromov found a new symplectic invariant called Gromov's invariant by studying the embedding of closed balls into a cylinder. This ground-breaking result opens a new era of the research of symplectic geometry. In this presentation, we explore the relationship between the homotopy type of the space of symplectic embeddings and the configuration space of $\mathbb{C}P^2$, focusing on the case of five balls.