Hofer Norms on Braid Groups and Quantitative Heegaard-Floer Homology

Given a lagrangian link with k components it is possible to define an associated Hofer norm on the braid group with k strands. In this talk we are going to detail this definition, and explain how it is possible to prove non degeneracy if k=2 and certain area conditions on the lagrangian link are met. The proof is based on the construction, using Quantitative Heegaard-Floer Homology, of a family of quasimorphisms which detect linking numbers of braids on the disc.