Floer homology for singular lagrangians and homological mirror symmetry of $CP^n$
I will explain how to define a version of Floer homology for Lagrangians with conical singularities and how, in good situations, this construction leads to the definition of localised mirror functors which generalise those of Cho-Hong-Lau. Then I will apply this construction to find the mirror of the pair $(CP^n, D)$ where $D={x_0=0} \cup {x_1...x_n=x_0^n }$. This is a joint work in progress with Georgios Dimitroglou Rizell.