Appears in collection : 2018 - T1 - WS1 - Model theory and combinatorics

In this talk I will give an overview of some recent developments on the interplay of model theory, hypergraph regularity and incidence combinatorics. We will focus on the notion of a distal structure and its local variants, which provide an abstract setting for “characteristic 0” incidence combinatorics. In particular, I will present joint work with David Galvin and Sergei Starchenko on generalizing various incidence bounds (e. g. the Szemer´edi–Trotter theorem, strong Erd˝os–Hajnal property, etc. ) from the semialgebraic setting to arbitrary distal structures (which includes o-minimal structures, p-adics, etc. ).