The Hanna Neumann Conjecture

The Hanna Neumann Conjecture (HNC) is a question about intersections of
subgroups in free groups; it has been open since 1956-57. Its strengthened version,
SHNC, was introduced by Walter Neumann. I will present a proof of SHNC.
The proof can be stated in an analytic language or purely combinatorially.
I will mostly concentrate on the combinatorial proof in this talk.
My plan is to give another talk at MPI later on about the analytic way
of stating SHNC, using l^2 Betti numbers. This allows generalizing the statement of SHNC and relates SHNC to the integral Atiyah Conjecture (AC), a question about the Murray-von Neumann dimension of kernels of operators given by matrices with entries in the group ring. AC is the analytic, and more general, version of the
Kaplansky's Zero-Divisors Conjecture.