## The New Zealand Mathematics Society Research Award

The

**New Zealand Mathematics Society Research Award**was instituted to encourage high quality mathematical research in New Zealand. The award is based on the previous five years mathematical publications of the winner either in books or recognised research journals. The judging panel is appointed by the President of the New Zealand Mathematical Society and the award is made annually at the New Zealand Mathematical Colloquium Dinner. A list of winners and the citations for their award follows:

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

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

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

**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.

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

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

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

**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.

**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.

**2018**Alex James. This award recognises Alex James for her contributions in mathematical modelling ranging from the theoretical, such as Lévy walks and complex ecological systems, to the very applied, such as masting and snail dynamics.