### 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.

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