Tame complexes, L2-invariants and the Hanna Neumann conjecture

I will talk about a joint article with Sam Fisher where we address the Hanna Neumann conjecture for limit groups. Roughly, its original formulation states that if G is a free group and H and K are subgroups of rank N and M, respectively; then the rank of the intersection is at most the product NM. Combining ideas of Antolin, Jaikin, Wilton and Wise (among others); we establish an analogous statement for any limit group by studying the geometry of its subgroups in relation to certain induced maps in L2-homology.