摘要：

In this talk we’ll focus on the Hamiltonian diffeomorphism group of the 2-sphere. This group has been studied by many symplectic geometers and it has been shown to have many nice properties. But there are still many open problems, including the equator conjecture. An equator on the 2-sphere is a smooth simple closed curve that divides the sphere into two complementary regions with equal area. The equator conjecture claimed that the set of equators equipped with the well-known Hofer’s metric is of infinite diameter. We will prove an alternative conjecture, where we replace “Hofer’s metric” with “quantitative fragmentation metric”. We’re using geometric group theoretical techniques to prove this alternative conjecture, which was mainly inspired by the study of the action of mapping class group on the curve graph by M.Bestvina and K.Fujiwara. This is a joint work with my supervisor, Richard Webb.