Department of Mathematics - Seminar on Pure Mathematics - Graph density inequalities

Graph limits is a recently developed powerful theory in studying graphs from a continuous perspective. In this talk, we will show it is undecidable to prove general inequalities of homomorphism densities into (edge weighted) graphs. Then I will show how the perspective of graph limits helps with graph homomorphism inequalities and how to make advances in a common theme in extremal combinatorics: when does randomness give nearly optimal bounds?