## Interview: James East

James East is a lecturer in pure mathematics at University of Western Sydney, Australia. His research interest includes transformation semigroups, partition monoids/algebras and dual symmetric inverse monoids. As for the computational aspect he is old skool, i.e. pen and paper, but he inspired many of the upcoming changes in the Semigroups package and the semigroup functionality of GAP.

**By training, are you a mathematician or a software engineer?**

Mathematician

**How did you become involved in computational semigroup theory?**

It would be lying to say I’m really involved in computational semigroup theory! But a few problems I’m interested in working on soon would benefit from some help from GAP.

**What is your main research/development at the moment?**

Most of my current research centres around partition monoids, a class of monoids that arise in representation theory, but contain many important semigroups including the full transformation semigroups, and the symmetric and dual inverse semigroups. Inspiration for research is largely taken from classical transformation semigroup theory. There are different flavours in the finite and infinite cases.

I’m also interested in semigroup analogues of Coxeter groups or, equivalently, Coxeter analogues of transformation semigroups – examples include reflection and dual reflection monoids (special cases being the symmetric inverse semigroup and the factorizable part of the dual symmetric inverse semigroup on a finite set).

**What is your perspective on using computers in mathematical research?**

If it works, then I see no problems! Really, I like to be able to do things by hand, check them by hand, etc, but obviously this is not always possible. If I was the programmer, I’d always wonder if there was an error in my code somewhere, but then again, we do rely on results from papers we might not have been able to check carefully. Actually, I think there are some very interesting questions on epistemology arising from the use of computers in mathematics…

**What do you do in your free time?**I have a 1yo son, so free time is not as plentiful as it used to be, but what time I do have is divided among cricket, guitar, piano, whisky appreciation, and blogging (about philosophy).

## Interview: James D. Mitchell

James D. Mitchell is a senior lecturer at University of St. Andrews, Scotland. He is the the developer of the Citrus package and also involved in the development of the Smallsemi package. On his homepage there are computer calculated and visualized examples of certain interesting transformation semigroups.

So, as the first post in the interview series, here are the Q&As.

**By training, are you a mathematician or a software engineer?**

Mathematician.

**How did you become involved in computational semigroup theory?**

I did a three year postdoc in St Andrews funded by a grant about computing with semigroups.

**What is your main research/development at the moment?**

At the moment, I’m mostly developing the Citrus package for GAP 4.5. The next release of Citrus (0.7) will include functions for computing with inverse semigroups of partial permutations. I think this is the first software package for this purpose, and I hope that Citrus 0.7 will facilitate research in this area much as other computational tools have done for permutation groups.

**What is your perspective on using computers in mathematical research?**

For some problems a computer is useless, for others it is essential or at the very least makes something that would be hard or impossible to do by hand possible. I think we should make use of whatever tools are available. Narrow mindedness is not a good problem solving strategy.

**What do you do in your free time?**

I’m a father, husband, runner, long distance cyclist, and prodigious cake-eater.