Turandom

Puccini's opera Turandot centers on three riddles, which the prince Calaf must answer correctly in order to avoid death. This talk won't be about opera, but it will feature three riddles in Ramsey theory: classical Ramsey numbers, Ramsey numbers of books, and Ramsey multiplicity constants.

At first sight, these riddles don't seem to have much to do with one another. However, they are tied together by the appearance and reappearance of two fundamental structures which crop up pretty much everywhere in Ramsey theory: the Turán coloring and the random coloring. In this talk, I'll discuss how these structures shed light on the three riddles, and tell you what we know about their answers (some), as well as what we don't know about their answers (a whole lot).

Based on joint works with David Conlon, Jacob Fox, and Xiaoyu He.