## NZMS Research Award

This annual Award was instituted in 1990 to foster mathematical research in New Zealand and to recognise excellence in research carried out by mathematicians in New Zealand. **This Award is based on mathematical research published in the last five calendar years (2013-2017). This could include research published in books, journals, other peer-reviewed venues, or other types of high quality mathematical research.** This assessment period may be adjusted to take into account an interrupted career pattern. To be eligible for the Award, a candidate must be a current member of the NZMS and must have been a resident of New Zealand for the last three years.

Nominations and applications should include the following:

- name and affiliation of candidate;
- statement of general area of research;
- a list of books and/or research articles published in the last five calendar years: 2013-2017;
- if appropriate, a justification for an adjustment of the assessment period to take into account an interrupted career pattern;
- an electronic copy (pdf) of each of the five most significant publications selected from the list above;
- a clear statement of how much of any joint work is due to the candidate;
- names of two persons willing to act as referees, though the judging panel may approach referees other than those nominated;
- the referees should be chosen carefully; in particular, they should not have a conflict of interest and they should be able to give scientific insight into the work to be assessed. It may be easier to avoid a conflict of interest by choosing international referees; and
- a citation, of maximum 40 words, summarizing the mathematical research underlying the application.

A judging panel will be appointed by the NZMS President, and the panel makes recommendations to the President for the Award. No person shall receive the Award more than once. The Award consists of a certificate including an appropriate citation of the awardee's work, and will be announced and presented at the New Zealand Mathematics Colloquium Dinner in December.

All nominations and applications should be sent by email to the NZMS President, Assoc Prof Vivien Kirk by 31 August 2018. Submissions should state clearly that they are for the NZMS Research Award.

Unsuccessful applicants from 2017 will be invited to update their application so that it can be reconsidered in 2018.

The Research Award for 2017 was presented at the NZ Mathematics Colloquium dinner in Auckland to **Igor Klep** of the University of Auckland for "deep and fundamental advances in real algebraic geometry and its application to diverse fields including operator theory, optimization, free analysis, convexity, and von Neumann algebras".

## NZMS Early Career Research Award

This award was instituted in 2006 to foster mathematical research in New Zealand and to recognise excellent research carried out by early-career New Zealand mathematicians. Applicants should be within seven years of confirmation of PhD, but an appropriate adjustment to this time period can be made to take into account an interrupted career pattern. **The candidate will be judged on their best three published research outputs and a two-page CV. Research outputs could include publications in books, journals, other peer-reviewed venues, or other types of high quality mathematical research.** To be eligible, the candidate must be a current member of the NZMS, and must have completed a significant part of their research in New Zealand.

Nominations and applications should include the following:

- name and affiliation of candidate;
- statement of general area of research;
- a two-page CV which illustrates their standing in their community;
- if appropriate, a justification for an adjustment of time since confirmation of PhD;
- an electronic copy (pdf) of each of their three best papers (the papers must be published or in press);
- a clear statement of the mathematical contribution of the candidate in cases of joint authorship;
- names of two persons willing to act as referees, though the judging panel may approach referees other than those nominated;
- the referees should be chosen carefully; in particular, they should not have a conflict of interest and they should be able to give scientific insight into the work to be assessed. It may be easier to avoid a conflict of interest by choosing international referees; and
- a citation, of maximum 40 words, summarising the mathematical research underlying the application (it is recommended that self-applicants approach a colleague to write this citation).

A judging panel will be appointed by the NZMS President, and makes recommendations to the President for the Award. No person shall receive the Award more than once. The Award consists of a certificate including an appropriate citation of the awardee's work, and will be announced and presented at the New Zealand Mathematics Colloquium Dinner in December.

All nominations and applications should be sent by email to the NZMS President, Assoc Prof Vivien Kirk by 31 August 2018. Submissions should state clearly that they are for the NZMS Early Career Award.

Unsuccessful applicants from 2017 who are still eligible in 2018 will be invited to update their application so that it can be reconsidered in 2018.

The Early Career Award for 2017 was presented at the NZ Mathematics Colloquium dinner in Auckland to ** Brendan Creutz ** (University of Canterbury) for "his outstanding work on local-global questions on diophantine equations, in particular his resolution of a 50 year old question of Cassels and the development of novel computational techniques to study the arithmetic of algebraic curves and surfaces".

## Kalman Prize for Best Paper

The Kalman Prize for Best Paper was instituted in 2016 to recognise excellence in research carried out by New Zealand mathematicians. The Prize will normally be awarded annually for an outstanding and innovative piece of research in the mathematical sciences published by a member or members of the NZMS. **The Prize is for a single publication of original research, which may be an article, monograph or book, having appeared within the last 5 calendar years: 2013-2017.** The value of the Prize is $5000. The Prize is generously funded by the Margaret and John Kalman Charitable Trust, and recognises the significant contributions to mathematics in New Zealand made by Professor John Kalman.

A publication may be nominated for the Prize by any member of the NZMS who is not an author of that publication. To be eligible, the nominated publication must have at least one author who:

- is a current member of the NZMS, and was a member in the calendar year of publication of the nominated work; and
- is a resident of New Zealand, and was a resident of New Zealand at the time when the research was carried out.

In the case of publications with multiple eligible authors, the Prize will be shared by all eligible authors. The existence of authors who do not meet the conditions in i) and ii) above will not preclude the award, although the judging panel may take into account whether the NZ author has made a major contribution to the published work. The judging panel may deem a publication ineligible if an author has previously received an award from the NZMS for a body of research that included the nominated publication.

A judging panel will be appointed by the NZMS President, and makes recommendations to the President for the Prize. The winner of the prize will be announced at the New Zealand Mathematics Colloquium Dinner in December.

Nominators should provide a brief summary of 1-2 pages of what makes the nominated publication important, innovative and outstanding (with appropriate references to prior or subsequent work in the field), and the names of three possible assessors. The judging panel may approach assessors other than those nominated. Assessors should not have a conflict of interest and they should be able to give scientific insight into the work to be assessed. It may be easier to avoid a conflict of interest by choosing international assessors.

All nominations should be sent by email to the NZMS President, Assoc Prof Vivien Kirk by 31 August 2018. Submissions should state clearly that they are for the Kalman Prize for Best Paper.

Unsuccessful applicants from 2017 will be invited to update their application so that it can be reconsidered in 2018.

The Kalman Prize for Best Paper in 2017 was awarded to **Lisa Orloff Clark** (Victoria University Wellington) for the journal article

Jonathan H. Brown, Lisa Orloff Clark, Cynthia Farthing and Aidan Sims. Simplicity of algebras associated to etale groupoids. Semigroup Forum 88 (2014), 433-452. |

## NZMS Aitken Prize (Student Prize)

The Society offers a prize for the best contributed talk by a student at the annual New Zealand Mathematics Colloquium. This prize is known as the Aitken Prize, in honour of the New Zealand born mathematician Alexander Craig Aitken. The Prize was first offered at the 1995 Colloquium held in conjunction with the Aitken Centenary Conference at the University of Otago. Candidates for the Prize give a talk on a topic in any branch of the mathematical sciences.

To be eligible, a candidate must be enrolled (or have been enrolled) for a degree in Mathematics at a university or other tertiary institution in New Zealand in the year of the award. The prize consists of NZ$500, accompanied by a certificate. Candidates should indicate their willingness to be considered for the Prize on the Colloquium registration form.

A judging panel is appointed by the NZMS President. The panel makes recommendations to the President for the Prize. Normally the Prize will be awarded to one person, but in exceptional circumstances the Prize may be shared, or no prize may be awarded.

The winner in 2017 was **Jesse Hart** of the University of Auckland for the talk "Notions of transfinite diameter on affine algebraic varieties".

The prize consists of a cheque for NZ$500, accompanied by a certificate.

## Recipients of the Research Award

2017 | Igor Klep | This award recognises Igor Klep for deep and fundamental advances in real algebraic geometry and its application to diverse fields including operator theory, optimization, free analysis, convexity, and von Neumann algebras. |

2016 | David Bryant | This award recognises David Bryant for work developing mathematical, statistical and computational tools for evolutionary biology, and work drawing on evolutionary biology to develop new theories in mathematics. |

2016 | Bernd Krauskopf | This award recognises Bernd Krauskopf for outstanding contributions to dynamical systems, especially bifurcation theory and its application to diverse physical phenomena. |

2015 | Hinke Osinga | This award recognises Hinke Osinga for pioneering work on theory and computational methods in dynamical systems and its applications in biology and engineering. |

2014 | Dimitri Leemans | This award recognises Dimitri Leemans for his striking contributions to algebraic combinatorics that combine techniques from algebra, graph theory, combinatorics and number theory for the exploration and classification of highly symmetric geometric structures. |

2013 | Steven Galbraith | This award recognises Steven Galbraith for applying deep ideas from number theory and algebraic geometry to Public Key Cryptography to achieve world leading processing speeds without compromising security. |

2012 | Ben Martin | This award recognises Ben Martin's outstanding and broad contributions to algebra including the application of geometric invariant theory to algebraic groups, the geometry of spherical buildings, and the representation growth of groups. |

2012 | Tom ter Elst | This award recognises Tom ter Elst for his deep and sustained contributions to the analysis and understanding of elliptic operators, and associated evolution processes. |

2011 | Shaun Cooper | This award recognises Shaun's sustained generation of significant and original contributions to number theory, particularly in the areas of elliptic functions, theta functions, and modular forms. |

2010 | Charles Semple | This award recognises Charles Semple’s landmark contributions to combinatorics, and in particular matroid theory, as well as leading work in phylogenetics and computational biology. |

2009 | André Nies | This award recognises André Nies’s special creativity and highly influential contributions in the area of mathematical logic and in particular its application to questions of computability, complexity, and randomness. |

2008 | Mike Hendy | For his innovative mathematical approach to molecular ecology and evolution which has transformed the field. His seminal work on the Hadamard transform—used to separate out pertinent signals in evolutionary data—is now an integral part of phylogenetic software internationally and has contributed to the solution of several fundamental problems |

2007 | Ernie Kalnins | For his wide ranging, prolific and significant contributions to mathematics, especially in his research on symmetries of partial differential equations, separable coordinates and superintegrable systems. |

2006 | Robert Aldred | For his leading work in Combinatorics and Graph Theory. In particular his near complete solution of the vertex colouring/edge partition problem, the characterisation of regular graphs which admit at most one 2-factor as well as his recent work on the Path Partition Conjecture from the early 80s by resolving (in the negative) a strong form of this conjecture. |

2006 | Mick Roberts | For his pioneering and practical work in Mathematical Epidemiology, his development of realistic physiologically based models of the incidence and spread of infectious diseases and his work on parasite transmission on pasture, all of which has attracted international recognition. |

2005 | Robert McLachlan | For creative, pioneering work leading to deep advances in the theory of geometric numerical integration, and its application in the study of dynamical systems. |

2005 | James Sneyd | For extensive and celebrated contributions in mathematical biology, demonstrating approaches that combine originality with biological realism. |

2004 | Eamonn O'Brien | For outstanding achievements in using computation, backed up by deep algebraic theory, to solve long-standing and difficult problems in group theory. |

2003 | Rod Gover | For highly original contributions in conformal differential geometry, that has led to the solution of some outstanding and difficult problems. |

2002 | Bakhadyr Khoussainov | For his contributions to computable model theory and the theory of automatic structures. |

2001 | Warren Moors | For his impressive body of interconnected research work on the geometry and topology of Banach spaces, related questions of set-theoretic topology and especially non-smooth analysis and optimization where a number of deep insights of a foundational nature have been achieved. |

2000 | Graham Weir | For his wide-ranging in-depth contributions to applied mathematical modelling covering a diverse range of phenomena including geosciences, structure of materials, corrosion theory, and the flow of granular material. |

1999 | Mike Steel | For his fundamental contributions to the mathematical understanding of phylogeny, demonstrating a capacity for hard creative work in combinatorics and statistics and an excellent understanding of the biological implications of his results. |

1998 | Jianbei An | For his contributions to the study of modular representations of groups, in which he has established his leading expertise through a combination of deep understanding, ingenuity and technical skill. |

1997 | Peter Lorimer | For a lifetime of achievements in mathematical research, especially for his contributions to the application of group theory in geometry and combinatorics, and to the structure and classification of finite projective planes. |

1996 | Mavina Vamanamurthy | For his prolific and far-reaching work in analysis and topology, especially for his contributions to the theory of quasiconformal mappings and special functions; contributions that are characterized by both analytic ingenuity and geometric insight. |

1996 | Geoff Whittle | For his work on matroids and other combinatorial structures, in which he has contributed fruitful ideas and found beautiful new results; placing him in the forefront of recent workers on difficult problems of matroid representation. |

1995 | Vladimir Pestov | For his creative and ingenious research in areas ranging from topological groups and Lie theory to the nonstandard analysis of superspace, in which he has solved long-standing open problems as well as demonstrating his breadth and depth of understanding and a gift for elegant and colourful exposition. |

1995 | Neil Watson | For an outstanding series of research articles on harmonic functions and potential theory, in which he has introduced new ideas and tools, and deep analyses, that have resulted in new and improved approaches to classical theorems and led to their generalisation to more abstract situations. |

1994 | Gaven Martin | For fundamental contributions in analysis, especially in complex analysis, requiring a careful and inventive blending of algebraic, analytic, and topological ideas, with applications in diverse areas ranging from differential equations, through hyperbolic geometric to low-dimensional topology. |

1993 | Marston Conder | For research exhibiting insight and originality in solving problems in algebra and combinatorics, in which, by his outstanding skills in machine computation, he has demonstrated the effectiveness of the computer when guided by real intelligence. |

1992 | Rod Downey | For penetrating and prolific investigations that have made him a leading expert in many aspects of recursion theory, effective algebra and complexity. |

1992 | Vernon Squire | For major contributions to the science of ocean wave-ice interaction, ranging from the theoretical and mathematical to the experimental and practical aspects, that have made him the leading consultant in this field |

1991 | John Butcher | For establishing new fundamental connections between analytic stability properties and algebraic properties of numerical methods for the solution of nonlinear differential equations; for implementing new methods; and for an outstanding monograph on Runge-Kutta and general linear methods. |

1991 | Rob Goldblatt | For outstanding work in generalisations and applications of modal logic, including four books displaying a remarkable mastery of diverse aspects of mathematics from programming to space-time geometry. |

## Recipients of the Kalman Prize for Best Paper

2017 | Lisa Orloff Clark | Jonathan H. Brown, Lisa Orloff Clark, Cynthia Farthing and Aidan Sims. Simplicity of algebras associated to etale groupoids. Semigroup Forum 88 (2014), 433-452. |

2016 | Gaven Martin | T. H. Marshall and G. J. Martin. Minimal co-volume hyperbolic lattices II: Simple torsion in a Kleinian group. Annals of Mathematics 176 (2012), 261-301. |

## Recipients of the Early Career Research Award

2017 | Brendan Creutz | For his outstanding work on local-global questions on diophantine equations, in particular his resolution of a 50 year old question of Cassels and the development of novel computational techniques to study the arithmetic of algebraic curves and surfaces. |

2016 | Alexander Melnikov | For highly original contributions to the theory of computability in algebra and topology. |

2015 | Adam Day | For fundamental contributions to the theory of algorithmic randomness and computability including the solution of the random covering problem. |

2014 | David Simpson | For his contributions to the analysis of the effects of randomness and uncertainties in nonsmooth dynamical systems. |

2013 | Florian Beyer | For his contributions to the understanding of the global structure of cosmological solutions of Einstein’s equations using numerical and analytical methods, and, in particular, for the proof of the wellposedness of the singular initial-value-problem for Fuchsian PDEs. |

2012 | Mark Holmes | For rapidly becoming a world expert in the theory of random walks, and in the analysis of high-dimensional models in statistical physics. |

2011 | Claire Postlethwaite | The award recognises Claire's enormous progress in applying mathematics to the study of animal movement, and for her development of fundamental ideas in applied dynamical systems. |

2010 | Mihály Kovács | For his innovative research in the field of stochastic partial differential equations, particularly their numerical approximation. |

2009 | Stephen Marsland | For outstanding work in many areas of computational and applied mathematics, including self-organizing networks, machine learning, image registration, and generalized Euler equations. |

2008 | Barbara Holland | For her groundbreaking work in interpreting information of historical and biological importance in comparisons of genetic sequence data, and for her pioneering development of phylogenetic networks that succeeded where simple optimisation models failed in identifying conflicts and in unmasking the more interesting biological evidence. |

2007 | Noam Greenberg | For his discovery of new natural definable classes which capture the dynamics of constructions arising from computability theory, his studies of real-valued measures on the continuum and his use of delicate inductive arguments to exhibit links between high compressibility and low computational power. |

2007 | Catherine McCartin | For her fundamental contributions to the development of efficient algorithms for computational problems in a variety of areas, and for her development of theoretical frameworks for parameterized counting problems and for parameterized approximation problems. |

## Recipients of the Aitken Prize

2017 | Jesse Hart | Auckland | Notions of transfinite diameter on affine algebraic varieties |

2016 | Naomi Chandler | Auckland | Pulse Dynamics of Fibre Lasers with Saturable Absorbers |

2015 | Andrew Keane | Auckland | Bifurcation analysis of a model for the El Niño Southern Oscillation |

2014 | Timm Treskatis | Canterbury | Accelerated gradient vs. primal-dual methods in nonsmooth optimisation |

2013 | Chris Stevens | Otago | The Friedrich-Nagy gauge for colliding plane gravitational waves |

2013 | Timm Treskatis | Canterbury | Trust-region SQP methods for numerical simulations of viscoplastic flows |

2012 | Stefanie Hittmeyer | Auckland | Untangling Wild Chaos |

2012 | Jennifer Creaser | Auckland | The Lorenz System Near the Loss of the Foliation Condition |

2011 | Edoardo Persichetti | Auckland | Coding theory and cryptography:New perspectives |

2010 | Rachael Tappenden | Canterbury | Extensions of compressed sensors |

2009 | Michael Smith | Auckland | Vibration of floating and submerged elastic plates |

2009 | Shannon Ezzat | Canterbury | Representation growth of the Heisenberg group over quadratic integers |

2008 | Mareike Fischer | Canterbury | Curious properties of Maximum Parsimony in estimating evolutionary trees and ancestral sequence states |

2007 | Peter Humphries | Canterbury | A basis exchange property for matroids |

2007 | Ratneesh Suri | Massey | A real options approach to fisheries |

2006 | Kevin Byard | Massey | Applications of qualified residue difference sets |

2005 | Amanda Elvin | Massey | The role of gap junctions in a neural field model |

2005 | Elan Gin | Auckland | Calcium waves and buffers |

2004 | Joanne Mann | Massey | To vaccinate or not to vaccinate? |

2003 | Cynthia Wang | Massey | Modelling a plate of arbitrary shape in infinitely deep water using a higher order method |

2002 | Sivajah Somasundaram | Waikato | Some recent results concerning weak Asplund spaces |

2001 | Brian van Dam | Auckland | The construction method of resolutions and Dowker spaces |

2000 | Patrick Rynhart | Massey | Static liquid bridges |

2000 | Barbara Holland | Massey | Median networks: A visual representation of ancient Adelie penguin DNA |

2000 | Sivajah Somasundaram | Waikato | Cover semi-complete topological groups |

1999 | Britta Basse | Canterbury | Mathematical modelling for conservation: predator control via secondary poisoning |

1999 | Jamie Sneddon | Auckland | Domination conditions for tournaments |

1998 | Charles Semple | Victoria | Excluded minors for matroid representability |

1997 | Robyn Curtis | Auckland | Subgraphs of hypercubes with no small cycles |

1997 | Louise Parsons | Auckland | |

1996 | Anton Raviraj | Massey | Gauss's equation and Backlund transformations |

1996 | Thomasin Smith | Massey | On arithmetic degree theory |

1995 | Chris Stephens | Canterbury | Global optimisation requires global information |