This is the third talk of the seminar series on "Fukaya categories associated to Lefschetz fibrations".

The Maslov index of a homotopy class of holomorphic discs determines the dimension of the moduli space of such discs in Floer cohomology. I am going to define the Maslov index for loops of Lagrangian subspaces and explain how to apply this notion to holomorphic discs.

In the second part of the talk, I will introduce the notion of graded Lagrangian submanifolds, and apply it to obtain a grading on Floer cohomology.