Abstract:
There has been a variety of recent progress on problems concerning the number of homomorphisms from a graph \(G\) to a fixed image graph \(H\). For instance if we know that \(G\) is regular of degree \(d\) and has \(n\) vertices, what is the maximum number of such homomorphisms? In particular the problem of enumerating independent sets fits into this framework and has been a motivating example. I will survey some of the known results and mention some recent work with Andrew Ray and (separately) Jonathan Cutler.