Embeddings of symplectic balls in $\mathbb{C}P^2$ and configuration spaces

Abstract: Existence of symplectic embeddings of $k$ disjoint balls of given capacites $c_1,\ldots, c_k$ into a given symplectic manifold is a central problem in symplectic topology. However, beside a few examples, very little is known about the space of all such embeddings. In this talk, I will discuss the case of rational $4$-manifolds of small Euler numbers, with a special attention to the minimal manifolds $\mathbb{C}P^2$ and $S^2\times S^2$. For rational manifolds, a very rich and intricate picture emerges that blends symplectic topology, complex geometry, and algebraic topology.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

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