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

I will describe lower bounds (i. e. constructions) for several hypergraph Ramsey problems. These constructions settle old conjectures of Erd˝os–Hajnal on classical Ramsey numbers as well as more recent questions due to Conlon–Fox–Lee–Sudakov and others on generalized Ramsey numbers and the Erdos–Rogers problem. Most of this is joint work with Andrew Suk.