Talk by Philippe Charron

One of the most well-known theorems in Sturm-Liouville theory is that, under dirichlet or Neumann boundary conditions, the n-th eigenfunction has exactly n interior zeroes. However, Sturm published in the same year a generalization of this result: any sum of eigenfunctions of indices between n and N had between n and N interior zeroes. I will discuss a generalization of this result to quantum graphs, which shows a clear distinction between the interval, general graphs and higher-dimensional manifolds.