### Programme of the Pure Mathematics Colloquium

The colloquium takes place on Thursdays at 4pm in Theatre C of the Mathematical Institute (unless indicated otherwise).

• 22nd Sept, 2016: Wolfram Bentz (Hull)
Title: The minimal generating sets of the semigroup of transformations stabilising a given partition
Abstract: Let $\mathcal{P}$ be a partition of a finite set $X$. We say that a transformation $f:X\to X$ stabilises the partition $\mathcal{P}$ if for all $P\in \mathcal{P}$ there exists $Q\in \mathcal{P}$ such that $Pf\subseteq Q$. Let $T(X,\mathcal{P})$ denote the semigroup of all full transformations of $X$ that preserve the partition $\mathcal{P}$.

In 2005 Pei Huisheng found an upper bound for the minimum size of the generating sets of $T(X,\mathcal{P})$, when $\mathcal{P}$ is a partition in which all of its parts have the same size. In addition, Pei Huisheng conjectured that his bound was exact. In 2009, Araújo and Schneider used representation theory to solve Pei Huisheng's conjecture.

A more general task is to find the minimum size of the generating sets of $T(X,\mathcal{P})$, when $\mathcal{P}$ is an arbitrary partition. In this talk we presents the solution of this problem and discuss some of the proof techniques, which range from representation theory to combinatorial arguments.

This is joint work with João Araújo (Universade Aberta/CEMAT), James Mitchell (University of St Andrews), and Csaba Schneider (Universidade Federal de Minas Gerais).
• 29th Sept, 2016: Zemer Kozlov (Warwick)
Title: TBA
Abstract: TBA
• 6th Oct, 2016: Xiong Jin (Manchester)
Title: TBA
Abstract: TBA
• 13th Oct, 2016: Gary McGuire (UCD)
Title: TBA
Abstract: TBA
• 3rd Nov, 2016: Sanju Velani (York)
Title: TBA
Abstract: TBA
• 10th Nov, 2016: Mirna Djamonja (UEA)
Title: TBA
Abstract: TBA
Past colloquia can be found here.