Limits of Dense Combinatorial Objects

The theory of limits of discrete combinatorial objects has been thriving for over a decade. There are two known approaches to it, one is geometric and semantic ("graph limits") and another is algebraic and syntactic ("flag algebras". The language of graph limits is more intuitive and expressive while flag algebras are more helpful when it comes to generalizations to combinatorial objects other than graphs, as well as to concrete calculations.
In this talk I will try to give a gentle introduction to the subject. Time permitting, I will talk about general ideas behind our joint research with Leonardo Coregliano attempting to build a unified theory using model-theoretical language and apply it to the study of quasi-randomness.