New paper on arXiv: Daniel Neuen and I show in Distinguishing Graphs by Counting Homomorphisms from Sparse Graphs that homomorphism counts from graphs of bounded genus do not distinguish graphs up to isomorphism. More generally, we show that homomorphism indistinguishability over any graph class of bounded vortex-free Hadwiger number is not isomorphism. Thereby, we make progress towards Roberson’s conjecture that homomorphism indistinguishability over any proper minor-closed graph class is not isomorphism. Finally, we show that that this conjecture fails when generalised to topological-minor-closed graph classes.