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Search Marsden awards 2008–2017

Search awarded Marsden Fund grants 2008–2017

Fund Type: Marsden Fund

Category: Fast-Start

Year Awarded: 2013

Title: Model theoretic techniques in Banach spaces and combinatorics

Recipient(s): Dr A Usvyatsov | PI | Victoria University of Wellington
Professor Sir S Shelah | AI | The Hebrew University of Jerusalem

Public Summary: Model theory applies techniques from mathematical logic to the analysis of arbitrary structures. My work lies in model theory of metric structures, and in dependent theories. The first part of the proposal is motivated by a very fundamental question in functional analysis: characterize Banach spaces that embed basic sequence spaces. I propose to address this question by applying recently developed tools of stability theory for metric structures. The second part is related to VC-theory in combinatorics, computational geometry, and machine learning. I propose to study VC-density of families of sets through its model theoretic discrete counterpart, dp-rank.

Total Awarded: $300,000

Duration: 3

Host: Victoria University of Wellington

Contact Person: Dr A Usvyatsov

Panel: MIS

Project ID: 13-VUW-107


Fund Type: Marsden Fund

Category: Standard

Year Awarded: 2008

Title: Modelling a virus

Recipient(s): Prof MG Roberts | PI | Massey University
Prof JAP Heesterbeek | AI | University of Utrecht

Public Summary: Viruses multiply and evolve within their hosts. A virus is in conflict with its host's immune system. Transmission of a virus to a new host, even one of the same species, introduces it to a different environment and different selection pressures. Transmission of a virus between hosts of different species may result in unexpected consequences for host or virus. Mathematical models will describe the within-host evolution and between-host transmission of a virus. Thought experiments carried out on the models will reveal how the virus's characteristics and environment determine how it spreads. The results will be related to HIV and influenza.

Total Awarded: $410,667

Duration: 3

Host: Massey University

Contact Person: Prof MG Roberts

Panel: MIS

Project ID: 08-MAU-046


Fund Type: Marsden Fund

Category: Fast-Start

Year Awarded: 2009

Title: Modelling gene trees in species trees and networks

Recipient(s): Dr JH Degnan | PI | University of Canterbury
Associate Professor EA Allman | AI | University of Alaska Fairbanks
Dr LKN Nakhleh | AI | Rice University

Public Summary: Evolutionary biologists are searching for the best ways to combine information from multiple genes in order to infer species-level relationships (phylogenetic trees), such as that humans are more closely related to chimpanzees than to gorillas. Although several methods have been proposed, little is known theoretically about whether many of these methods have a sound statistical justification. The current project will determine properties of distributions of evolutionary trees inferred for different genes (gene trees) by using the powerful tools of algebraic statistics. These can be used to determine whether methods have a sound basis or reasons that a method might fail.

Total Awarded: $250,667

Duration: 3

Host: University of Canterbury

Contact Person: Dr JH Degnan

Panel: MIS

Project ID: 09-UOC-045


Fund Type: Marsden Fund

Category: Fast-Start

Year Awarded: 2012

Title: Modelling paradoxes in non-classical mereotopology

Recipient(s): Dr ZJ Weber | PI | University of Otago

Public Summary: Logical paradoxes have beset our best philosophical theories for millennia. Philosophical logic in New Zealand is emerging internationally for innovative responses to these problems. However, the very existence of seemingly unsolvable rational dilemmas remains completely unexplained. This project will give a new description of logical paradoxes, explaining them through mathematical models based on non-classical logics. The hypothesis is that paradoxes are conceptual boundaries, as shown in an intuitive geometric way by a formal theory of connected parts (mereotopology). The goal is to advance on the very idea of paradox, newly rendered in precise terms that facilitate philosophical progress.

Total Awarded: $300,000

Duration: 3

Host: University of Otago

Contact Person: Dr ZJ Weber

Panel: HUM

Project ID: 12-UOO-200


Fund Type: Marsden Fund

Category: Standard

Year Awarded: 2013

Title: Modelling the extensive and intensive margins in earnings dynamics

Recipient(s): Professor DR Hyslop | PI | Victoria University of Wellington
Professor DE Card | AI | University of California, Berkeley

Public Summary: Characterising individual earnings dynamics is a key factor in many economic research and social policy contexts, such as understanding savings and asset demand, and understanding income inequality and the role of income support programmes. Most panel data studies of individual earnings dynamics implicitly focus on the intensive (wage and hours) margin of variation, and ignore the extensive (employment) margin of adjustment. This project will develop models of individual and family earnings processes that incorporate both margins of adjustment. We will extend existing dynamic models of earnings dynamics to integrate dynamic discrete choice models for the employment decision.

Total Awarded: $608,696

Duration: 3

Host: Victoria University of Wellington

Contact Person: Professor DR Hyslop

Panel: EHB

Project ID: 13-VUW-071


Fund Type: Marsden Fund

Category: Standard

Year Awarded: 2014

Title: Modelling, inference and prediction for dynamic traffic networks

Recipient(s): Professor ML Hazelton | PI | Massey University
Professor HK Lo | AI | The Hong Kong University of Science and Technology
Professor MJ Smith | AI | University of York
Professor DP Watling | AI | University of Leeds
Professor GE Cantarella | AI | University of Salerno

Public Summary: Traffic congestion is a worldwide problem. In New Zealand alone, the cost of road congestion is estimated to be around $1 billion per annum through its impact on the economy, the environment, and public health. Models that describe the day-to-day dynamics of road traffic networks provide the means for development and testing of durable remedial measures, and hence play a critical role in transport management and planning. However, current day-to-day traffic models have been underused, partly because their theoretical properties are insufficiently flexible to capture many facets of real network behaviour, and also because we lack tools necessary for their effective practical implementation.

In response, our overall aim is to develop and analyse an extended class of day-to-day dynamic models that is better able to capture the types of spatial and temporal variation in patterns of traffic flow that are seen in practice, and to design appropriate statistical methods to ensure that model fitting and assessment is reliable. This work will provide robust tools to examine how knowledge of drivers' behaviour today might be used to predict patterns of traffic flow in the future, and how traffic systems will adapt to changes to the road network (e.g. road closures).

Total Awarded: $380,000

Duration: 3

Host: Massey University

Contact Person: Professor ML Hazelton

Panel: MIS

Project ID: 14-MAU-017


Fund Type: Marsden Fund

Category: Standard

Year Awarded: 2012

Title: Modern analysis and geometry

Recipient(s): Prof GJ Martin | PI | Massey University

Public Summary: This proposal sits at the forefront of two central areas of modern mathematics; nonlinear analysis and low dimensional topology & geometry; unified by themes in conformal geometry and geometric function theory.

We attack important longstanding problems with wide ranging applications. These include the classification of conformal dynamical systems on manifolds and their dynamically defined invariants. This project interacts with our novel results in geometric group theory. We investigate the structure and classification of arithmetic hyperbolic orbifolds extending our solution of Sigel’s1945 problem by developing new methods to attack key problems in hyperbolic geometry.

We develop fundamentally new models in nonlinear materials science for the study of the failure of materials through stretching and tearing. These have medical applications through the deformation of cellular structures and thereby modeling heart form and function. Preliminary work has been validated and is now extended as part of this project.

This latter research is partly informed through and underpinned by our recent advances in geometric function theory and surprising connections with harmonic maps in general metrics (suggesting new approaches to the Schoen conjecture) and other novel techniques developed by us to study Nitsche type phenomena.

Total Awarded: $534,783

Duration: 3

Host: Massey University

Contact Person: Prof GJ Martin

Panel: MIS

Project ID: 12-MAU-044


Fund Type: Marsden Fund

Category: Standard

Year Awarded: 2015

Title: Modern analysis and geometry

Recipient(s): Professor GJ Martin | PI | Massey University

Public Summary: This proposal links central and active areas of modern mathematics; nonlinear analysis and low dimensional geometry. It attacks longstanding important problems with wide application. We exploit unexpected connections discovered by us between extremal (minimisation) problems for scale invariant measures of energy and distortion with harmonic mappings in variable metrics. A particular focus is the development of an Lp Teichmuller theory interpolating between the classical and harmonic approaches. This suggests a new approach to the 2D Schoen conjecture, and novel application in the geometry and compactification of moduli spaces of Riemann surfaces. Applications in theoretical materials science and critical phase phenomena arise as distortion functionals are natural measures of change and address fundamental questions relating microstructure and length scales. The proposal also seeks to solve longstanding problems in low dimensional topology and geometry. Our previous work solving Siegel's 1945 problem on minimal covolume lattices provides new techniques and ideas to attack longstanding problems in the geometry of discrete groups. Not only are there completely novel applications relating knot theory and the structure of low dimensional moduli spaces, but the classification problem for generalized triangle groups and the identification of the Margulis constant seem now within reach.

Total Awarded: $545,000

Duration: 3

Host: Massey University

Contact Person: Professor GJ Martin

Panel: MIS

Project ID: 15-MAU-037


Fund Type: Marsden Fund

Category: Standard

Year Awarded: 2010

Title: Molecular mechanism of spreading of microbial pathogens: studies with the bacterium Listeria monocytogenes

Recipient(s): Dr KP Ireton | PI | University of Otago

Public Summary: Many microbial pathogens actively promote their spreading from infected human cells to surrounding cells. Overall, spreading mechanisms are not well understood. The bacterial pathogen Listeria monocytogenes is an important cause of food-borne illnesses in humans and animals. Cell-cell spread of Listeria in the host intestinal epithelium is likely critical for disease. Our recent findings indicate that Listeria spreads through a novel process involving dissipation of tension at cell junctions. Listeria perturbs these junctions through a virulence factor called InlC. Our proposed research will test the hypothesis that InlC affects junctions and Listeria spreading by binding the human protein Sec31A, thereby interfering with protein trafficking from the endoplasmic reticulum to the Golgi. This work will provide novel insights on how pathogens spread, and may identify new pathways regulating cell junctions.

Total Awarded: $682,609

Duration: 3

Host: University of Otago

Contact Person: Dr KP Ireton

Panel: BMS

Project ID: 10-UOO-015


Fund Type: Marsden Fund

Category: Fast-Start

Year Awarded: 2015

Title: Molecular metamorphosis: new synthetic methods and design

Recipient(s): Dr T Fallon | PI | Massey University

Public Summary: Small carbon-based molecules are defined by a static network of covalent bonds between atoms. Fluctional molecules break this definition and exist in constant metamorphosis. This extraordinary behaviour derives from rearrangment reactions which transpose valency within the molecule. While these systems have been curiosities for many years, their unique properties remain unexploited. This project will advance the field in two ways: It will improve the synthetic methodology of the Bullvalene structure, and explore a completely new family of linear fluctional molecules.

Bullvalene is a remarkable structure, which spontaneously radiates out all substituents connected to it, in all possible relative arrangements. By devising new and simple ways to control the substitution pattern around this structure, we will be able to advance principles of adaptive binding, and from there develop new types of sensors and drug discovery tools.

We will also design and demonstrate a new class of walking molecules, based on linear cascade rearrangements, whereby a molecular fragment can walk along the greater structure. This work will develop the synthetic methods, and begin to study the fluctional nature of these novel systems. From this knowledge, we will design new molecular devices.

Total Awarded: $300,000

Duration: 3

Host: Massey University

Contact Person: Dr T Fallon

Panel: PCB

Project ID: 15-MAU-154


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