# Pure Maths Colloquium: Katherine Staden

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

Where: | Lecture Theatre D |

When: | Oct 4 2018 @ 16.00 |

Video: | Not recorded |

Speaker: | Katherine Staden University of Oxford |

Title: | Erdős–Rothschild problems in graphs, groups and the integers |

I will discuss Erdős–Rothschild type problems in discrete structures, in which we seek to maximise the number of non-Ramsey colourings. That is, the number of colourings of a discrete structure such that every colour class does not contain some forbidden substructure. For example, maximise the number of \(r\)-colourings without monochromatic

- \(k\)-cliques among all \(n\)-vertex graphs;
- Schur triples among all subsets of a given abelian group;
- Schur triples among all subsets of \(\{ 1,\ldots,n\}\).

I will give an overview of the area, the number- and graph-theoretic tools which go into the proofs, and discuss some joint work with Oleg Pikhurko and Zelealem Yilma, and with Hong Liu and Maryam Sharifzadeh.