Computation in geometric and combinatorial group theory
In July 2016, ICMS hosted a workshop on Computation in geometric and combinatorial group theory
Bringing together experts in the theoretical and practical aspects of algorithms and decision problems in combinatorial and geometric group theory, this workshop aimed to instigate a more coherent approach to future developments in these areas. The workshop included participation from younger mathematicians working in geometric group theory and computational group theory, with the hope of inspiring them to work in this newly developing area.
As a result of this workshop it is anticipated that there will be both a significant increase in the quality and quantity of user-friendly software, and the strengthening of theoretical results, by making them more precise and applicable.
Delegates at the Computation in geometric and combinatorial group theory workshop 2016
There were 36 delegates at the workshop and they had a full week with lots of talks and networking opportunities. On the Tuesday evening, Alexei Miasnikov (Stevens Institute of Technology) gave a public lecture entitled What is the world we live in? Mysteries of computing.
Alexei Miasnikov asking the audience to consider a world of Algorithmia
Whilst the workshop was on, we took the opportunity to speak to the delegates in a bit more detail.
Eamonn O'Brien, University of Auckland
Eamonn grew up in Ireland, before undertaking a PhD at the Australian National University in Canberra. He had research fellow positions in Germany and Australia before taking a permanent position at the University of Auckland in 1997. Enjoying life in the Southern Hemisphere, he has been there ever since. He has recently finished a term of office as Head of Department and is currently on a 6 month sabbatical in Europe.
Tell me about today's event and your role in it
I am a participant in the workshop, I have worked in this area over many years, particularly on developing algorithms for the study of finitely-presented groups and their quotients, and their implementation and application to answer questions about such groups.
What brought you to this area of research?
Inevitably, you are influenced by people you work with. I was lucky to study and later work with someone who was a key player in the development of algorithmic aspects of groups, including those finitely-presented. I learned a lot from him. It is a challenging area with hard problems and few well-developed tools. There are many problems for which no algorithms exists. But there are some good techniques which can be applied which sometimes provide an answer. I’m instinctively drawn to problems that are concrete! Challenging problems push us to work harder.
Other than exploring maths, what are the benefits of taking part?
The real benefit is finding out what others are doing formally and informally. Formally through the talks and presentations. The informal interactions are the key and very useful. As a group, we have quite disparate backgrounds, theoretical and computational perspectives. The computational communities don’t necessarily know the key questions the theoreticians are grappling with, and the theoreticians don’t always know the range of techniques and machinery available. It is a 2 way-street between these communities. I am always keen to work on questions and problems of interest to others and I have identified some of these.
What will you take back to your [day job/research/studies]?
Quite specific challenges at some level. There have been some very specific examples of ‘here is what I want to do, can you develop a technique?’ As well as this, the workshop enhances your knowledge. Learning about new results is very important, particularly finding out things you don’t normally encounter because they lie outside your normal area of research. This can influence your research in the medium and longer term.
Have you met interesting people, and if so, what connections have you made?
I have listened to a number of interesting talks which have led to interesting conversations. I’ve learned a lot, particularly about what challenges others are working on, which problems remain unsolved.
Do you have any advice for first-time ICMS attendees?
Interact, grab the opportunities to speak to others. Be open to conversations and risk speaking to people. Don’t be afraid to speak to people who are nominally ‘senior’ to you. Be willing to co-operate and collaborate out of your area. Part of my success as a mathematician has been to work with people who have different skills from me, it leads to interesting and sometimes better research.
Have you been to many other conferences? How does ICMS differ?
I attend a fair number of meetings, which range in size. This meeting is at the smaller end regarding number of participants. I prefer smaller meeting, with ca. 30-50 participants as you have more chance to meet people with overlapping interests. However it is important to make sure that meetings are not too narrow in focus.
If you could solve one maths problem, what would it be?
I would like to find a polynomial time algorithm to decide isomorphism of finite p-groups.
Do you have any thoughts regarding how we can raise the profile of maths?
Similar to ICMS, in Auckland we run a public lecture programme, which can help. We have 2-3 talks a year, and aim to have a big name, known outside of the maths community.
Do you have any thought on how diversity in mathematics can be improved?
You can ensure a programme of workshops has a good balance of speakers/delegates/organisers and provide good Role Models. But it is important not to be tokenistic. Encourage people to think carefully about invitees to meetings and ensure you provide young people with good opportunities to participate.
Who is your favourite mathematician and why?
John Horton Conway, I admire his ability to take simple concepts and use them to develop profound mathematics. Also, his ability to communicate with everybody, but particulary to engage teenagers in mathematics.