Title:  Sparse - dense dichotomy

What is a sparse graph or structure? We present a possible answer to this question in a form of Nowhere Dense versus Somewhere Dense dichotomy. This very robust dichotomy, which can be characterized in several different ways, generalizes many concrete problems and has consequences for several algorithms such as restricted coloring and model checking. The talk is based in part on the book Sparsity, Graphs, Structures, and Algorithms, Springer 2012, co-authored with Patrice Ossona de Mendez.