# News

Keep up to date with the latest news from the School of Mathematics and Statistics.

### New Professor Explores Multiplicity of Mathematics

The freezing of sea ice and exploding rocks in volcanoes may not sound like things a mathematician would worry about, but a newly-appointed Professor says mathematics has taken him on a 40-year academic journey of discovery.

As part of his inaugural lecture held 5 April 2016 to mark his professorial promotion, Victoria University of Wellington Professor Mark McGuiness will shed light on some of the interesting puzzles he has faced during his career. “I studied physics and worked my way through to applied and industrial mathematics,” says Professor McGuinness. “I’ve had the good fortune to work on a range of problems, including how to cook crispy cereals, how fast sea ice freezes, and why volcanic eruptions are sometimes very lumpy.” During the lecture Professor McGuinness will outline how mathematics provided the tools to solve these problems. In July, Professor McGuinness is codirecting Mathematics in Industry New Zealand 2016, a forum for researchers to look at applying mathematics, statistics, physics and engineering principles to problems brought by local businesses and industry. From a young age he was interested in solving puzzles and problems, says Professor McGuinness. “This curiosity continues to drive my research today. It’s really rewarding brainstorming and then solving a problem. I’d encourage anyone with an interest in problem solving to consider mathematics in their studies or as a career.”### Rod Downey Founder of International Conference series CCR

Rod Downey is a founder, with Veronica Becher in (Buenos Aires, Argentina) and Denis Hirschfeldt (Chicago), of the international conference series Computability, Complexity and Randomness (CCR), first held in 2004 and an annual event since 2007.

Rod is also on the conference series steering committee. http://math.hawaii.edu/wordpress/ccr-2016/conference-series/ The 2016 meeting was recently held in Honolulu and Rod will be co-editor of the proceedings, due to appear in the journal Theory of Computing Systems. Among the invited speakers at the meeting were current postdoctoral fellow Linda Brown Westrick and lecturer Dan Turetsky - further evidence of the strength of Victoria University in this exciting research area.A local tv show was made about the CCR conference in Hawaii and can be seen here:

https://www.youtube.com/watch?v=1kTtBlYbk9s

### What does detecting gravitational waves mean?

On 15 February 2016 two of Victoria's astrophysics researchers presented a seminar about the first direct observation of gravitational waves from the merger of two black holes.

The first ever direct observation of gravitational waves from the merger of two black holes was announced by researchers at the LIGO Scientific Collaboration. Their 20 year search for gravitational waves—ripples in the fabric of space-time—confirms a prediction of Albert Einstein’s theory of general relativity just over a century ago. So what exactly does this big breakthrough mean? Victoria’s Professor Matt Visser, a world-leading expert in general relativity, and Associate Professor Melanie Johnston-Hollitt, an internationally prominent radio astronomer, shared their insights on how it was discovered, what it means, and the future of astrophysics. Professor Visser’s research looks at the areas of general relativity, quantum field theory, and theoretical cosmology, and Associate Professor Johnston-Hollitt is co-author on the paper describing the electromagnetic follow-up observations of the gravitational wave source. You can see the presentation here: https://youtu.be/cbVmoGsQuko### More Maths Marsden Magic

Two mathematicians are among the 25 Victoria academics to be awarded Marsden Fund research grants in the 2014 round.

Dimitrios Mitsotakis has been awarded a Fast Start grant (for early career researchers). His project is entitled "Numerical solution of time-dependent multi-dimensional nonlinear dispersive wave equations with applications to coastal hydrodynamics”. He explains the goal of the project as follows. The mathematical modeling of water waves continues to attract great interest in the scientific community, including mathematics, physics, and engineering. Models that describe water waves are systems of nonlinear partial differential equations. Computing the solutions of these systems requires efficient and accurate numerical methods. Our objective is to develop a theoretical and computational research framework through which we will systematically address wave systems. The new tools will improve the speed and the accuracy of tsunami early-warning systems, which are critical for mitigating the devastating effects of tsunamis. Matt Visser is a world-renowned expert on the theory of gravitation. This will be his fourth Marsden project and it concerns "The final stages of the Hawking evaporation of black holes”. Stephen Hawking predicted in 1974 that black holes are not entirely black - they emit radiation and slowly evaporate due to subtle quantum effects. The final stages of this process, when the black hole has become relatively small, continue to generate heated debate and confusion among experts, even after 40 years of intensive research. Matt plans a renewed attack on this problem, based on a three-fold approach: investigating the types of horizon that can occur and their implications for the internal structure of black holes, investigating the quantum energy conditions and the properties of any resulting spacetime singularities, and finally a careful analysis of both the differences and similarities between black-hole and ordinary thermodynamics. These projects bring to 34 the number of Marsden grants on which Victoria mathematicians and statisticians have been principal investigators, in the 20 years the Fund has been running. The total value of those grants is in excess $12.5M. This remarkable ongoing record places the School of Mathematics, Statistics and Operations Research at the forefront of Victoria’s leading research standing in New Zealand.### Researcher solves 40 year old problem

## Victoria researcher solves 40 year-old math problem

A Victoria University of Wellington mathematician has experienced his own eureka moment, solving a 40 year-old mathematical problem. Professor Geoff Whittle, from Victoria’s School of Mathematics, Statistics and Operations Research, has been working with colleagues Professor Jim Geelen (Canada) and Professor Bert Gerards (Netherlands) to solve a problem posed by the famous mathematician and philosopher Gian-Carlo Rota in 1970. Earlier this year the trio realised that, after more than 15 years of work, they had achieved all the essential ingredients to prove Rota’s Conjecture. Geoff visited the United Kingdom last month to break news of the discovery to mathematics colleagues at a conference where he was a guest speaker. Rota’s Conjecture relates to a specialised area of mathematics known as matroid theory, a modern form of geometry, which Geoff specialises in. Rather than focusing on distance and angles, matroid theory investigates properties of structures which don’t change under projection—for example, whether or not three points are always on a line, or four points are on a plane. The theory investigates geometric structures that can be completely different from those in our world, and Rota’s Conjecture is a way of using mathematics to recognise these alternative structures. “I like to compare it to Kafka’s Metamorphosis story, where a man wakes up and realises he has transformed into an insect—the way he views the world changes entirely,” says Geoff. “Matroid theory is all about visualising a world of new geometrical structures and developing ways of describing the big, overarching structures which would emerge.” Although he has been working on proving Rota’s Conjecture for a long period of time, Geoff says the hard work will really begin now, as the team starts writing up the results of its work. “Resolving Rota’s Conjecture is really special, and the product of many, many years of collaborative work. “Now, we have a lot of writing to do, which I expect to take several more years—as well as many hundreds of pages of journal articles.” “It’s a little bit like discovering a new mountain—we’ve crossed many hurdles to reach a new destination and we have returned scratched, bloodied and bruised from the arduous journey—we now need to create a pathway so others can reach it.” Head of School Dr Peter Donelan is also excited about the news, which he believes will attract international recognition. “This will be regarded as one of the outstanding mathematical achievements in recent years,” he says. Geoff has been based at Victoria University since 1992, when he joined the School of Mathematics, Statistics and Operations Research as a lecturer. He was promoted to Reader in 1997 and to Professor in 2001. Geoff is recognised as a world leader in the field of discrete mathematics. He has spent time as a visiting research fellow at Merton College, Oxford and is a Fellow of the Royal Society of New Zealand. In 1996, his achievements were recognised with the New Zealand Mathematical Society’s Research Award. For more information, contact Professor Geoff Whittle, phone 04-463 5650 or email geoff.whittle@vuw.ac.nz. Watch a video of Geoff talking about his career and research here: www.youtube.com/watch?v=Lw8D15amE_4### Jonathan Crook PhD completion

Congratulations to Jonathan Crook on completing his Phd on "Ice growth and platelet crystals in Antarctica". Jonathan completed his PhD under the supervision of Dr Mark McGuinness.

### Estate Khmaladze in collaboration with West Virginia University

Congratulations to Professor Estate Khmaladze who has been appointed consultant to a 2 year United States NSF funded project: Recovery of Functions via Moments: Hausdorff case awarded to West Virginia University.

### Rod Downey appointed to Marsden Council

The Minister for Research, Science and Technology Wayne Mapp has appointed Professor of Mathematics Rod Downey to the Marsden Fund Council.

Professor Downey was awarded a James Cook Fellowship in 2008 and was the inaugural Maclaurin Fellow at the New Zealand Institute for Mathematics and its Applications (NZIMA) CoRE. He is a Fellow of the Royal Society of New Zealand and the only New Zealand-based mathematician to give an invited lecture at the International Congress of Mathematicians. His role on the Marsden Fund Council is to provide guidance on investments made by the fund in leading-edge research projects. He will convene the Mathematical and Information Sciences panel. The Marsden Fund Council comprises ten eminent researchers - a Chair and nine convenors. Each heads a panel in their academic field. Panels work to assess applications for funding of research projects.### PhD Scholarship in Image Recognition Available

A PhD Vice-Chancellor's Strategic Research Topic Scholarship for "Particle Swarm Optimization for Image Recognition" is available under the supervision of Dr Mark Johnston.

Image recognition tasks arise in a wide variety of practical situations, e.g., detecting faces from video images, identifying suspected terrorists from fingerprint images and diagnosing medical conditions from X-rays. Particle Swarm Optimization (PSO) is a stochastic, population-based evolutionary algorithm for solving optimization problems (in Operations Research) and image classification problems (in Artificial Intelligence). PSO uses ideas analogous to biological evolution and social-psychological principles of behaviour to search the space of candidate solutions for a particular task. PSO has been applied to a variety of image recognition and optimisation tasks and has achieved a certain level of success. However, there are still limitations in particle topology and representation, search algorithms and feature discovery in PSO that restrict PSO for difficult image classification tasks. Scholarships applications close on 15 May and application forms will be available shortly from the Scholarships website. Interested applicants should complete the application form, and also contact Dr Mark Johnston.