# 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 http://theran.lt/pure-colloquium/.

 Where: Lecture Theatre D When: Oct 4 2018 @ 16.00
 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.