James East
*University of Western Sydney
***The Brauer project: Enumeration of idempotents in partition monoids
**

Partition algebras arise in representation theory and statistical mechanics. They may also be constructed as twisted semigroup algebras of the partition monoids, a natural class of diagram semigroups that canonically embed the full transformation semigroups, symmetric inverse semigroups, and more. In this talk, I’ll report on joint work with Igor Dolinka, Athanasios Evangelou, Des FitzGerald, Nick Ham, James Hyde and Nick Loughlin on the enumeration of idempotent partitions.

Bob Gilman
*Stevens Institute of Technology
***Small Cancellation Theory and Hyperbolic Groups.
**

Various classes of small cancellation groups provide many examples of word hyperbolic groups. The goal of this talk is to go in the opposite direction, that is, to characterize hyperbolic groups as groups admitting presentations which satisfy conditions similar to small cancellation conditions.

Murray Elder
*(University of Newcastle, Australia)
***An algebraic generating function for permutations generated by a stack of depth 2 and infinite stack in series
**

The set of permutations generated by a passing an ordered sequence through a stack of depth 2 followed by an infinite stack in series was shown to be finitely based by Elder in 2005. In this new work we obtain an algebraic generating function for this class, by showing that the class is in bijection with an unambiguous context-free grammar. This is joint work with Geoffrey Lee.

Colva Roney-Dougal
*(University of St Andrews)
***TBA
**

Chris Jefferson
*(University of St Andrews)
***How to Efficiently Intersect Permutation Groups and Related Problems
**

Finding the intersection of permutation groups is a fundamental building block of computational group theory, but the area has been woefully understudied over the years. In this talk I will give an overview of mathematical basis of the current state of the art in this area, and the open areas of research where better mathematics would lead to faster intersection techniques.

Tara Brough
*(University of St Andrews)
***TBA
**

Markus Pfeiffer
*(University of St Andrews)
***Parallelising backtrack search in permutation groups
**

Chris Jefferson
*(University of St Andrews)
***Minimal and canonical images in permutation groups
**

Minimal and canonical images are a central part of the efficient implementation of many CGT algorithms, but have been poorly studied this far.

I will discuss the two main algorithms in this area -- finding the minimal image of a set by Steve Linton, and finding a canonical image of a graph by Brendan McKay. I will show how both of these techniques can be generalised to handle a much larger range of objects, including sets of sets, partitions and transformations. I will also discuss the open problems in the area.

Rosemary Bailey
*(University of St Andrews)
***Entropy, partitions, groups and association schemes II
**

Peter Cameron
*(University of St Andrews)
***Entropy, partitions, groups and association schemes I
**

Maximilien Gadouleau
*(Durham University)
***The algebra of memoryless computation
**

An elementary problem when writing a computer program is how to swap the contents of two variables. Although the typical approach consists of using a buffer, this operation can actually be performed using XOR without memory. In fact this approach can be generalised to compute any function without memory (hence the term memoryless computation). In this talk, we translate problems in memoryless computation in terms of transformation semigroups or permutation groups. This allows us to study how fast and how easily any function can be computed without memory.

Collin Bleak
*(University of St Andrews)
***Groups of sliding block code automorphisms
**

Peter Cameron
*(University of St Andrews)
***Poly-Bernoulli numbers and acyclic orientations
**

Andrew Francis
*(University of Western Sydney)
***Bacterial genome evolution with algebra
**

The genome of a bacterial organism consists of a single circular chromosome that can undergo changes at several different levels. There is the very local level of errors that are introduced through the replication process, giving rise to changes in the nucleotide sequence (A,C,G,T); there are larger scale sequence changes occurring during the lifetime of the cell that are able to insert whole segments of foreign DNA, delete segments, or invert segments (among other things); and there are even topological changes that give rise to knotting in DNA.

In this talk I will describe how algebraic ideas can be used to model some bacterial evolutionary processes. In particular I will give an example in which modelling the inversion process gives rise to new algebraic questions, and show how algebraic results about the affine symmetric group can be used to calculate the ``inversion distance" between bacterial genomes. This has applications to phylogeny reconstruction.