Geometry Colloquium: Hofer Norms on Braid Groups and Quantitative Heegaard-Floer Homology (Francesco Morabito)

Time： 16:30-17:30

Place：Faculty of Science Building  #3, Room 204

Speaker：Francesco Morabito（ETH Zürich）

Title：Hofer Norms on Braid Groups and Quantitative Heegaard-Floer Homology

Abstract：Given a Lagrangian link with k components in the disc (or k+g components on a surface with non-empty boundary and genus g), it is possible to define an associated Hofer norm on the braid group with k strands. Starting from basic definitions such as those of Hofer metrics, braids and Lagrangian links, we are going to give a sketch of the proof of this result. The main tool is going to be Quantitative Heegaard-Floer Homology (as constructed by Cristofaro-Gardiner, Humilière, Mak, Seyfaddini and Smith), which gives rise to families of quasimorphisms detecting linking numbers of braids. This talk is based on my own work for the case of the disc, and a joint work with Ibrahim Trifa for the extension to higher genus.