Complexity Monotonicity of Counting Problems

This talk presents recent results on the complexity of counting induced subgraphs from the perspective of parameterized and fine-grained complexity theory. In particular, we will introduce and discuss "Complexity Monotonicity", a novel and powerful tool due to Curticapean, Dell and Marx, which provides a unifying view on problems that require to count small structures in large networks, subsuming graph homomorphisms, embeddings and induced subgraphs.