Geometry Seminar

For some quantitative problems in symplectic geometry, one can reduce the main difficulty to classifying certain singular algebraic curves. In the case of the complex projective plane these curves are now fairly well understood, but even for other simple del Pezzo surfaces there is whole complicated zoo of such curves. In this talk, I will explain how the formalism of cluster algebras gives a beautiful way of systematically organizing and understanding unicuspidal curves. In particular, they are organized into the exchange graph of an associated cluster algebra, obstructions to stabilized ellipsoid embeddings. This is based on joint work in progress with D. McDuff.