In today’s **Higher Ed Daily Brief**: message for mathematicians

**Don’t be afraid**

US mathematician **Julie Rowlett **is the star attraction at the **Australian Mathematical Sciences Institute** winter school, which is on this month at the distinctly warm climate of the University of Queensland’s Brisbane campus.

Professor Rowlett — whose interests also encompass languages, the Korean martial art of Tang Soo Do, scuba diving, making and listening to music, dancing and cooking — is giving five lectures at the school to post graduate students and early career researchers from around Australia.

Her message? “Don’t ever be afraid of mathematics! Even the “mathematics professionals’’ get stuck, make silly mistakes, and need to ask for explanations of things we have trouble understanding. There is mathematics in basically everything, even if we don’t understand it all yet.”

For her the “everything” includes cooking (how and why does a square pan cook differently to a round pan?) and plankton (can we describe mathematically how they swim and compete for food?)”

Professor Rowlett, who has an appointment at Sweden’s Chalmers Institute of Technology in Gothenburg, is giving a public lecture this evening (July 9) at 6.30pm at the Abel Smith lecture theatre on the University of Queensland’s St Lucia campus.

**Original article appeared in The Australian newspaper on 9 July 2018. Author: Tim Dodd**

We interviewed Associate Professor Mariel Saez from Pontificia Universidad Catolica de Chile to find out what drives her interest in mathematics and advice she has for future researchers.

**Can you tell us about your work? What drives your interest in this field?**

I work on geometric analysis. I am interested in the connection between the geometry of objects (i.e. shape, size, etc) and their analytic properties. In physics and nature in general, several phenomena are described in terms of partial differential equations or minimisation of certain energy functionals, which are often considered and studied as analytical objects. On the other hand, the physical nature of the problems allow to interpret these operators geometrically and study them from that perspective. In my opinion, establishing such connection enriches both the analytical and the geometric point view.

**What are your favourite applications of your work?**

I don’t know much about “real world” applications, but I am really curious about them. Within mathematics, it is really exciting to see questions that seem not analytical or geometric to be solved with techniques of these fields (for instance, the Poincare conjecture)

**What are some other areas of your field that are particularly interesting to you?**

Mathematics is so broad that to understand areas of mathematics that are far from mine is difficult. I would be very interested in learning more about other techniques that are used, for instance, in algebraic geometry or number theory.

**Why did you become a mathematician?**

I always liked maths and felt confortable working with numbers. I enjoy the challenge of facing a question and being able to solve it. As a professional mathematician, these questions often take much longer to solve (sometimes years or sometimes never), which can be frustrating at times, but still coming to a solution is very satisfying

**Do you have any advice for future researchers?**

To be patient and, if they enjoy research, to pursue their own ideas. It may feel like it takes a long time to become a mathematician, but I really like the fact that one is always learning new things.

**Why are opportunities such as AMSI Winter School so valuable? What do you hope attendees take from your lectures?**

I think it is a great opportunity to have the chance of interacting with mathematicians from all over the world . I hope the attendees learn about problems that they did not know befeore.

*Associate Professor Saez will be presenting the topic Curvature Flow of Networks at the 2018 Winter School, hosted by The University of Queensland.*

We interviewed Dr Paul Bryan from Macquarie University about the path he took to becoming a mathematician, and his favourite applications of his work.

**Can you tell us about your work? What drives your interest in this field?**

My research focuses particularly on non-linear, geometric evolution equations such as the Ricci Flow and the Mean Curvature Flow where one deforms a geometric structure via a gradient flow to decrease an energy in the fastest way possible. This is a classic technique in the calculus of variations, used here to determine optimal, or canonical geometric structures. Such methods have enjoyed considerable success in modern times, with the famous resolution of the Poincaré Conjecture and Thurston Geometrisation Conjecture classifying the structure of three-dimensional spaces modelling the universe in which we live as well as the Riemannian Penrose Inequality relating the mass in the universe with the area of Black Holes.

A simple illustrative example is that of a soap bubble; upon blowing a soap bubble, it’s shape evolves according to reducing the surface tension as fast as possible which in turn depends on how the bubble is curved. As we all know, the soap bubble becomes spherical which is the desired canonical geometry – the curvature is constant everywhere.

I can’t really explain what “drives my interest”. I just enjoy working on these problems. I never really planned to work in my field – there was just a sequence of events starting with an undergraduate summer research project that lead to honours, PhD. and so on. I can’t say I really think much about why I do what I do. I simply enjoy doing it and seem to be reasonably proficient at it.

**What are your favourite applications of your work?**

Like G.H. Hardy, I don’t really think a good deal about the applications of my work. Unlike Hardy however, I don’t proudly announce that there are no applications of my work! I don’t know that anyone has used my work for anything outside mathematics, but who knows what may occur in the future.

Right now I’m interested in exploring the landscape as it were; adding a little to humanities understanding of non-linear geometric problems. This is how much of mathematics developed – some was immediately of interest to applications and some was just for the sake of understanding. It’s very difficult to estimate the impact of such “pure mathematics” as it only becomes clear over time – possibly centuries!

**Why did you become a mathematician?**

Just following my nose so to speak. I left high school in year 11, got bored and so went to TAFE. I chose my course (electronics) because I was disorganised so most courses had closed enrolment by the time I got around to enrolling. I picked something that sounded interesting out of what was left was and only required a year 10 certificate. Fortunately I both enjoyed it and did well and it lead into me studying TV/VCR and PC servicing and the software development.

I got a job working repairing computer monitors which led to repairing PC’s and laptops and to providing IT tech support. Then I got a job administering GNU/Linux systems at TAFE (the same one I originally learnt how to from!) and became interested in hacking the Linux kernel so I went to university to study computer science.

I hadn’t taken any calculus before and I had to take first year maths. I found this tremendously more interesting than the computer science so I switched to mathematics and the rest is as they say history.

The turning point that led me to work in my field was when I enrolled in a summer research program. The coordinator of the program at the time was Ben Andrews. I had taken his analysis course and done reasonably well so when I asked him about potential projects and supervisors, he suggested I work with him. We studied Huisken’s paper on distance comparison for the curve shortening flow and discussed various ways to interpret and extend the result. This led to my honours project and then Ph.D. project.

**Do you have any advice for future researchers?**

I’m not entirely sure I am qualified to give advice! I didn’t make any plans to become a researcher – it just sort of happened naturally. I was lucky in that I just did whatever seemed interesting at the time and it all worked out. My dad used to say “it will be there when you need it”. I guess that’s my main advice. Try not to worry too much. If you like what you do, you’ll put in the time and effort because it’s not a chore, it’s more like an enjoyable hobby

*Dr Bryan will be presenting the topic Comparison Geometry at the 2018 Winter School, hosted by The University of Queensland.*

**The University of Auckland**

We interviewed Professor Rod Gover from The University of Auckland about what motivated him to become a mathematician, and what his biggest achievements are to date.

**Why did you become a mathematician?**

As a young child, and then at high school, I was passionately interested in science and where it could take us. At that stage I liked mathematics puzzles and some competitions but did not think of mathematics as a vocation. But then in my last years of high school and at university my interests focused on general relativity and theoretical physics, and suddenly I found myself wanting to deeply understand the mathematics behind all of these things. Then I became excited by the fact that in mathematics one can quickly discover new things and move theory along.

**Do you have any advice for future researchers?**

Push hard to get to the bottom of whatever it is you are working on. It is my feeling that the strongest results and progress come also with simplifying perspectives, and that these are seen when one understands the problem in a broad framework.

**Why are opportunities such as AMSI Winter School so valuable? What do you hope attendees take from your lectures?**

Learning the mathematics in a given area by only reading research articles can be difficult and slow. In any school like this the presenters make a big effort to quickly but accurately distill out some of the main points and exciting directions in new research.

**What do you consider your biggest achievement to date?**

The discovery of new approaches to constructing geometric structures, geometric operators, curvatures and invariants, and then the use of these approaches to find such objects.

*Professor Gover will be presenting the topic Curvature in Conformal Geometry at the 2018 Winter School, hosted by The University of Queensland.*

**Chalmers University of Technology, Sweden**

Associate Professor Julie Rowlett from Chalmers University of Technology takes some time out to tell us about her research passions and gives us a little taste of what to expect at the Public Lecture.

*Can you tell us about your work? What drives your interest in this field?*

My work is at the interface of geometry and analysis. The analysis comes primarily from physics. For example, many people know the equation which says that force is equal to mass times acceleration. This is a mathematical equation! We use analysis to understand the mathematical equations of physics. Now, let’s think a little more about this particular equation, like for example the force of an accelerating car. The geometry surrounding the accelerating car affects the physics. For example, if we try to accelerate on ice, the car might just spin out, and not move forwards. So, if we really want to understand the physics, we need to think about both the mathematical analysis of the physical equation together with where this is happening. The “where” (like on ice, on a dirt or gravel road, on a paved road, etc) is the geometry. I have an insatiable curiosity to understand this interface where geometry and analysis interact.

*Do you have any advice for future researchers?*

I would (perhaps rather boldly) say that the two most important qualities of a researcher are diligence and humility. Natural talent is overrated. If you’re passionate about a subject and willing to dedicate your time to it, that is more important than having innate talent for the subject. Don’t be afraid to ask questions or admit that you don’t understand something! Be honest about what you do (and do not) understand.

*Why are opportunities such as AMSI Winter School so valuable? What do you hope attendees take from your lectures?*

The AMSI Winter School is an excellent and rare learning opportunity! Four researchers will come from around the world and share our knowledge about four topics, each in our particular area of expertise. My goal is to teach you as much as I can in the time we have about heat and its relationship to geometry. I aim to give both a broad and general overview of the topic as well as go into further particulars in the areas of my expertise, where I can tell you both what experts know, as well as what we do **not **know. It is a rather unique opportunity, because I’ve created my course especially for this winter school. To the best of my knowledge, some of the course content is not found anywhere in the literature.

*What do you consider your biggest achievement to date?*

Computing the incomputable.

This may sound a bit weird, so let me get more down-to-earth. There are mysterious numbers which are responsible for many important physical phenomena including: the sounds caused by vibrations, the way waves travel, the flow of heat, and the energy of quantum particles. Important as they are, in general, we are unable to compute them exactly. Together with my research partners, I have proven a small collection of results about these “incomputable numbers.” These results translate nicely into everyday terms. With Zhiqin Lu, we proved that “one can realistically hear the sound of symmetry,” in a certain sense. With Zhiqin Lu and later generalizations with Medet Nursultanov and David Sher, we proved that “one can hear corners.” If you’re curious about what this really means in a bit more precise mathematical and physical formulation, then come to the public lecture!

*Associate Professor Rowlett will be presenting the topic Heat Flow and Geometry, as well as the Public Lecture The Spectrum: Incomputable yet physically tangible numbers at the 2018 Winter School, hosted by The University of Queensland. *

AMSI Winter School 2017 was hosted and held at the Queensland University of Technology. With the theme of Computational Foundations of Data Science, the event was held from the 26th June to 7th July.

71 graduate students, postdoctoral fellows and early career researchers from around Australia and the world attended the intensive two-week vacation residential school.

The diverse program provided participants with opportunities to advance their subject knowledge and build collaborative networks with their peers. Students also enjoyed being exposed to fields and topics outside of their specialist research area throughout the two weeks, and attended many of the program extras.

The AMSI Winter School is funded jointly by the Department of Education and Training and the Australian Mathematical Sciences Institute, with support from:

- Queensland University of Technology
- QCIF
- ACEMS
- The Simulation Group
- SGI
- TechnologyOne
- BHP Billiton Foundation (part of the ChooseMaths Grant initiative).

*“This event continues to be a great success on many levels, and has proven, yet again, to be a valuable experience for Australia’s next generation of mathematicians and cognate researchers.”*

**Professor Ian Turner
**

**BAYESIAN INFERENCE & DATA ASSIMILATION**

- Introduction to Bayesian Computational Methods via Markov Chain Monte Carlo Algorithms – Dr Chris Drovandi, Queensland University of Technology
- Data Assimilation: A Mathematical Introduction – Dr Kody Law, Oak Ridge National Laboratory / University of Tennessee

**HIGH-DIMENSIONAL STATISTICS**

- Model selection and inference for high-dimensional data – Dr Davide Ferrari, The University of Melbourne

**INVERSE PROBLEMS**

- Bayesian Approaches for Inverse Problems and Optimal Experimental Design – Associate Professor Youssef Marzouk, Massachusetts Institute of Technology

**MACHINE LEARNING**

- A Decision Making View of Machine Learning – Dr Hanna Kurniawati, The University of Queensland
- Martingales, McDiarmid and Machine Learning: How to validate models like a pro! – Dr Brendan van Rooyen, Queensland University of Technology

**NONLINEAR OPTIMISATION**

- Optimisation Techniques For Data Analysis – Professor Stephen Wright, University of Wisconsin-Madison

**NUMERICAL LINEAR ALGEBRA**

- Large Scale Matrix Problems – Dr Linda Stals, Australian National University

**MODELS, MATHS AND THE REVOLUTION IN WEATHER FORECASTING**

The AMSI Winter School Public Lecture is run annually in conjunction with BrisScience and engages a broad audience with the topic of the school.

**MEDIA COVERAGE**

An AMSI Winter School 2017 program highlight, Dr Peter May’s public lecture received strong national and international media coverage. Australian, US and UK coverage revealed the impact of maths, science and super computers on the scale and capability of his team’s research at the Bureau of Meteorology. Reaching over 140 million people, see links below to some of this coverage.

*4 July, News.com.au, Benedict Brook, Weather forecasting looking years of even decades into the future could soon be a thing (Syndicated Nationally and Internationally)*

*5 July 2017, Daily Mail, Tim Collins, Computer Models Make Life Saving Weather Predictions*

*5 July 2017, Newsmax, Cathy Burke, Math, Science, Computers Spur Extreme Weather Forecasting Revolution*

The annual Winter School Women in Maths networking event was held in conjunction with the AustMS Women in Mathematics Special Interest Group on Wednesday, 28 June 2017.

The free event highlighted the contribution of women in Mathematics, raised awareness about issues for women in mathematics, and provided a forum for discussion of career pathways.

Three guest speakers joined over 50 attendees at the Queensland University of Technology who openly shared their experiences studying mathematics, and their subsequent careers:

- Amy Hawke (Brisbane State High School)
- Olivia Hutchinson (Boeing Defence Australia)
- Distinguished Professor Kerrie Mengersen (Queensland University of Technology)

AMSI Winter School 2016 was hosted and held at the University of Queensland from the 4th to 15th July, with a Biological and Environmental Modelling theme. 45 graduate students, postdoctoral fellows and early career researchers from around Australia attended the intensive two-week vacation residential school.

The diverse program provided participants with opportunities to advance their subject knowledge and build collaborative networks with their peers. Students also enjoyed being exposed to fields and topics outside of their specialist research area throughout the two weeks, and attended many of the program extras.

The AMSI Winter School is funded jointly by the Department of Education and Training and the Australian Mathematical Sciences Institute, with support from The University of Queensland, QCIF, ACEMS, The Simulation Group and the BHP Billiton Foundation (part of the Choose Maths initiative).

**Dr Phil Isaac
**

**OUR SECOND BRAIN: MODELLING ITS DEVELOPMENT AND DISEASE**

- Prof. Kerry A Landman, The University of Melbourne

**THE MATHEMATICAL MODELLING OF CHEMOTAXIS AS A MECHANISM FOR STRUCTURE AND PATTERN IN CELL POPULATIONS**

- Prof. Graeme Pettet, Queensland University of Technology

**THE DYNAMICS OF CALCIUM: THE INTERACTION OF MODELLING AND EXPERIMENTS**

- Prof. James Sneyd, The University of Auckland

**INTRODUCTION TO THE MATHEMATICS OF ENVIRONMENTAL DECISION SCIENCE**

- Dr Eve McDonald-Madden, The University of Queensland
- Prof. Hugh Possingham, The University of Queensland

**IS SCIENCE ANY USE FOR SAVING SPECIES AND HABITAT?**

Environmental conservation is a big challenge facing our planet. Isn’t it time to stand up and take action, rather than do more research? Why shouldn’t we just use the knowledge we already have to save threatened species?

Professor Hugh Possingham (Director of the ARC Centre of Excellence for Environmental Decisions) discussed the value of monitoring and information for achieving nature conservation outcomes and used decision science tools (optimisation) as the framework for deciding what research is useful.

The AMSI Winter School Public Lecture is run annually in conjunction with BrisScience and engages a broad audience with the topic of the school.

**MEDIA COVERAGE: ****Great Barrier Reef: Government must choose which parts to save, says expert**

*THE GUARDIAN – Saturday, 9 July 2016*

AMSI Winter School speaker Professor Hugh Possingham says authorities must confront the prospect that some parts of reef are doomed and focus on what to preserve with the Guardian:

‘Governments must decide which parts of the Great Barrier Reef they most want to save and confront the prospect that some of it may be doomed, an expert on conservation modelling has warned. University of Queensland professor Hugh Possingham said agencies, including the Great Barrier Reef Marine Park Authority, needed to make tough decisions about which parts of the natural wonder are most worth preserving “rather than trying to save everything”‘. Read more…

The annual Winter School Women in Maths networking event was held in conjunction with the AustMS Women in Mathematics Special Interest Group on Wednesday, 6 July 2016. This free event highlighted the contribution of women in Mathematics, raised awareness about issues for women in mathematics, and provided a forum for discussion of career pathways.

Three guest speakers joined over 50 attendees at the Science Learning Centre at the University of Queensland who openly shared their experiences studying mathematics, and their subsequent careers:

- Julia Bruerton (Brisbane Grammar School)
- Ellie Foxcroft (Biarri)
- Professor Kerry A Landman (University of Melbourne)

The 2015 Winter School on Algebra, Geometry and Physics was hosted by the University of Queensland. Forty graduate students and postdoctoral fellows from Australia and around the world came together at the university for the intensive two-week school. The exciting program gave participants the opportunity to learn from leaders in the field, expand their skills and build networks.

**GEOMETRIC REPRESENTATION THEORY**

- Assoc. Prof Anthony Henderson, University of Sydney
- Dr Masoud Kamgarpour, University of Queensland
- Dr Tony Licata, Australian National University

**MODUI SPACES IN SYMPLECTIC GEOMETRY**

- Dr Joan Licata, Australian National University
- Dr Brett Parker, Australian National University

**MOONSHINE CONJECTURES AND VERTEX OPERATOR ALGEBRAS**

- Prof Terry Gannon, University of Alberta
- Dr Nora Ganter, University of Melbourne
- Prof Geoffrey Mason, University of California Santa Cruz

**K-THEORY AND ITS APPLICATIONS**

- Dr Vigleik Angeltveit, Australian National University
- Dr Pedram Hekmati, University of Adelaide

**PROFESSOR GEOFFREY MASON**

Geoffrey is Distinguished Professor of mathematics at the University of California, Santa Cruz. He has worked in many areas of mathematics and became interested in modular functions when the Monstrous Moonshine conjectures were announced in 1979. Geoffrey then spent the first half of the 1980s initiating a systematic study of modular functions associated with finite groups. These works eventually led him to study the theory of vertex operator algebras which was the focus of his talk.

**PROFESSOR TERRY GANNON**

Terry is currently Professor of Mathematics at the University of Alberta, Canada, where he has been since 1998. He is an eminent mathematician with research interests in a wide range of mathematics, in particular the interactions of algebra, number theory, complex analysis, geometry and mathematical physics, with a focus on conformal field theory. He is the author of a popular monograph on *Moonshine beyond the Monster* (Cambridge University Press, 2006) which, together with more recent developments, formed the basis for his lectures on the Moonshine Conjectures and Vertex Operator Algebras course.

**THE GLASS BEAD GAME: PUBLIC LECTURE**

Professor Arun Ram, The University of Melbourne, took the audience on a virtual tour of a toy store with friends Maria Callas, Alexander Grothendieck and Hermann Hesse. Showing the audience pleasant games with glass beads, athletic games skiing the moguls, and violent games where everything gets smashed. The talk told stories related to current research in symmetry.

A networking event was held in conjunction with the AustMS Women in Mathematics Special Interest Group, the event supports the network and raises awareness about issues for women in mathematics.This year female mathematicians from The Australian National University, SilverRail, National Australia Bank and The University of Melbourne opened the event by talking about their experiences. The presentations were followed by lively discussion among attendees.

*“The lectures were at the same time fast paced and packed with knowledge, but at the same time comprehensible and pulled you along.”*

– Ross Ogilvie, The University of Sydney

*“I enjoyed the variety of lecturers and topics that were presented. We were also given ample time to spend with the lecturers to ask questions and chat.”*

– Jeremy Nugent, The University of New South Wales

**OPINION PIECE**: AMSI Winter School speakers Joan and Anthony Licata explained the importance of fundamental research to ABC Science:

“Mathematicians certainly weren’t thinking about computer graphics in the 1890s. They were studying abstract questions about two-dimensional geometry and developing beautiful mathematics. Nevertheless, the techniques they invented in order to state this question precisely and then answer it have turned out to be extremely useful. In fact, this theme recurs throughout human history: mathematics developed to solve abstract problems turns out to be useful. Maybe not always and definitely not quickly, but it happens over and over again. Read more…

The AMSI Winter School is funded jointly by the **Department of Education and Training**, the **Australian Mathematical Sciences Institute**, with support from The University of Queensland, Australian National University, Biarri, the Pacific Institute for the Mathematical Sciences, AMSI Intern & QCIF.

The 9th Annual Winter School was held from 7 – 18 July 2014 at the University of Queensland. The theme of this year’s School was Contemporary Aspects of Cryptography. The Winter School is aimed at postgraduate students and postdoctoral fellows in the mathematical sciences and cognate disciplines. The Winter School aims to enable participants to broaden and deepen their mathematical knowledge, and to build collaborative networks with other PhD students and early career researchers.

A series of mini-courses were offered over the two-week long School. The courses in the first week were more introductory in nature, allowing the courses in the second week to lead into current research problems. The courses covered a range of topics in the broad area of cryptography and were offered by eminent national and international researchers.

**Week 1
Program – Introductory Courses**

Provable Security of Cryptographic Primitives & Protocols

By Dr Douglas Stebila, Queensland University of Technology

The Human Side to Cryptography

*By Associate Professor Benjamin Burton, The University of Queensland*

Finite Fields

*By Dr Joanne Hall, Queensland University of Technology *

Applications of Coding & Information Theory to Cryptography

*By Assoicate Professor Serdar Boztas, RMIT University *

**Week 2
Program – Advanced Courses **

The Cryptomathematics of Bitcoin

*By Dr Brett Witty, Defence Science Technology Organisation *

Techniques in Cryptographic Implementation

*By Dr Zoltán Bácskai, Defence Science Technology Organisation*

Curves & Discrete Logarithms

*By Porfessor Tanja Langer, Technische Universiteit Eindhoven, Netherlands*

Quantum Cryptography

*By Dr Alessandro Fedrizzi, The University of Queensland*

New Mathematical Problems Arising from Cryptographic Research

*By Dr Alexei Miasnikov, Stevens institute of Technology, U.S.A*

2013 was the International Year of the Mathematics of Planet Earth, and the 8th annual AMSI Winter School took this as its theme. The Winter School is aimed at post-graduate students and postdoctoral fellows in the mathematical sciences and cognate disciplines. The Winter School aims to enable participants to broaden and deepen their mathematical knowledge, and to build collaborative networks with other PhD students and early career researchers.

A series of mini-courses were offered over the two-week long School. The courses in the first week were more introductory in nature, allowing the courses in the second week to lead into current research problems. The courses covered a range of topics in the broad area of the mathematics of planet earth, and were offered by eminent national and international researchers.

**Program – Introductory Courses **

Numerical Methods on GPUs

*By Vivien Challis, The University of Queensland*

Large-scale Inversion for Geophysical Exploration

*By Lutz Gross, Queensland University of Technology *

Dynamical Systems and Singular perturbations

*Peter Van Jeijster, Quenssland University of Technology*

**Program – Advanced Courses**

Mathematical Modelling of Infectious Diseases

*By Geoff Mercer, Australian National University *

Regularization of Inverse Problems in Geomathematics

*By Volker Michel, Universität Siegen*

Dynamics of Earthquake Rupture

*By Louise Olsen-Kettle, The University of Queensland *

Optimisation for Nature Conservation

By Hugh Possingham, The University of Queensland

For more information please visit The University of Queensland website here