URA Seminar - Thomas Lesgourgues

Title: On the use of senders in Ramsey Theory

Abstract: In this talk I will introduce and investigate some parameters in Graph Ramsey theory, beyond the traditional Ramsey numbers. A crucial ingredient for their analysis is the existence of gadget graphs, called signal senders, that were initially developed by Burr, Erdős and Lovász in 1976. I will explain their origin, properties, and try to convey their surprising strength. Using probabilistic methods, we will see how to build such gadgets, and how to use them to prove some theorems, previously out of reach without these tools.