Research Highlights
This page is highlights a selection of the funded research achievements in the school. The highlighted projects are testament to the diversity of research in the school, as well as the breadth of applications supported by the research, from internet security to mitigation of coastal flooding.
Project: NIMBUS³ - A Next-Generation Integrated Model for Better and Unified Storm Surge Simulations
Dr Nicole Beisiegel, mentored by Prof Frederic Dias
Funder and Scheme: Irish Research Council, Postdoctoral Fellowship
Project Description: This project NIMBUS³ deals with the investigation and development of numerical tools for storm surge and flood simulations. The focus is on the methodological study of a number of computational aspects that are widely beyond current operational capabilities with the aim to eventually inform their improvement. One particular focus is on adaptive mesh refinement, i.e. the distribution of dynamically changing localised resolution in order to increase computational efficiency and reduce computing time of storm surge simulations. Furthermore, algorithms for hazard- and risk assessment are developed to systematically quantify flood damage and to improve the predictive skill of computational flood models.
Twitter: @NicoleBeisiegel
Project: On the factorization of p-adic L-functions
Dr Daniele Casazza, mentored by Dr Kazim Buyukboduk
Funder and Scheme: Irish Research Council, Postdoctoral Fellowship
Project Description: The groundbreaking ideas of (opens in a new window)Deligne, (opens in a new window)Grothendieck and (opens in a new window)Langlands reshaped the field of Number Theory in the second half of 20th century, where L-functions emerged as one of the fundamental gadgets in the arithmetic study of algebro-geometric objects. The celebrated (opens in a new window)Birch and Swinnerton-Dyer Conjecture (BSD), one of the Clay Millenium Problems, concerns elliptic curves and is an instance of this broad philosophy. This project concerns p-adic analytic counterparts of these L-functions, which are defined in terms of intricate congruences that these transcendental objects exhibit. They are amenable to deformation and as such, they hold the gateway to BSD and its incarnations.
The impetus for research in number theory comes from within pure mathematics and yet, number-theoretic research offers important practical applications. For example, (opens in a new window)internet security dwells heavily on number-theoretic results that were originally discovered while pursuing theoretical goals. This project targets fundamental theoretical questions that concern p-adic L-functions and aims to lay the groundwork for future progress.
Kazim Buyukboduk’s (opens in a new window)research page
Project: HIGHWAVE
Professor Frederic Dias
Funder and Scheme: European Research Council (ERC) Advanced Grant
Project Description: HIGHWAVE covers simultaneously past, present and future energetic ocean waves. The project research, associated with sustainable environmental science and technology, will help future generations to improve environmental practice. HIGHWAVE is a cutting edge mathematical project that uses real-time raw data harvested in situ by the project team to develop new models and new algorithms. These new models will provide information about air and water exchange in oceanic environments, boulder deposits, erosion and structural damage.
(opens in a new window)highwave-project.eu
Project: RESOURCECODE – Project on Resource Characterisation to Reduce the Cost of Energy through Coordinated Data Enterprise
Professor Frederic Dias
Funder and Scheme: OCEANERA-NET CoFund (European Commission)
Project Description: OCEANERA-NET COFUND is an initiative of eight national and regional government agencies from six European countries. Key objectives are to maintain and grow Europe’s world leading position in ocean energy, help bring innovative low carbon energy solutions closer to commercial deployment, drive down the levelised cost of energy (LCoE), create growth and jobs and reduce the environmental impact of the energy system. RESOURCECODE aims to support investment and growth in the wave and tidal energy sector through the creation of an integrated marine data toolbox. The toolbox will consist of modelling and software tools, which will be made available via a new online platform. The toolbox is due to be launched in 2021 using 30 years of model data, creating the highest resolution wave model in North West Europe. The toolbox will enable world leading resource characterisation, which will allow technology developers and supply chain companies to improve engineering designs and optimise operations in highly demanding marine environments, increasing the confidence of potential investors.
(opens in a new window)RESOURCECODE
Project: Integrable Random Structures
Professor Neil O’Connell
Funder and Scheme: European Research Council (ERC) Advanced Grant
This project aims to develop and study integrable / exactly solvable models in probability. Examples of such models include interacting particle systems, random polymers, random matrices and various combinatorial models related to the theory of symmetric functions and Young tableaux. A common theme is some underlying algebraic structure which accounts for the integrability of the model in question. The project has a strong emphasis on models of representation-theoretic origin, particularly in the context of the theory of Young tableaux and its vast generalisations. For example, there is a remarkable connection between a birational version of the celebrated Robinson-Schensted-Knuth correspondence and GL(N)-Whittaker functions; moreover, this connection may be applied to the study of a class of random polymer models which belong to the so-called KPZ universality class of random matrix theory. The resulting theory has been substantially developed within the context of this project, including extensions to models with additional symmetries and also non-commutative versions. Some other recent developments include: a new approach to the study of moments of random matrices, connections between random matrices and SLE, progress on random sorting networks, and scaling limits for Whittaker measures.
(opens in a new window)Integrable Random Structures
Project: A Spatial Machine Learning Model for Analyzing Customers' Lapse Behaviour in Life Insurance
Dr Adrian O’Hagan
Funder and Scheme: Zurich Insurance and Enterprise Ireland, Innovation Partnership
Project Description: In this project we investigated if the incorporation of publicly available demographic information at population level, via census data, is useful in modelling customers’ lapse behaviour (i.e. stopping payment of premiums) in life insurance policies, based on data provided by an insurance company in Ireland. From the insurance company’s perspective, by identifying and assessing such lapsing risks in advance, the company can engage to prevent such incidents, save money by re-evaluating customer acquisition channels, and improve capital reserve calculation and preparation. Spatial analysis is typically used to investigate spatial patterns or to identify spatially-linked consumer behaviours in insurance, and incorporating such analysis in lapse modelling is expected to improve lapse prediction. Therefore, a hybrid approach to lapse prediction is proposed -- spatial clustering using census data is used to reveal the underlying spatial structure of customers of the Irish life insurer, in conjunction with traditional statistical models for lapse prediction based on the company data.
Project: ThermaSMART
Dr Lennon Ó’Náraigh
Funder and Scheme: European Commission Marie Skłodowska-Curie Research and Innovation Scheme
Project Description: The UCD School of Mathematics and Statistics is one of the partners in the EU-funded project ThermaSMART. ThermaSMART is an international and intersectoral network of organisations working on a joint research programme in the area of phase-change cooling of microprocessors and high-power electronic devices. Overall responsibility for coordinating the network lies with the University of Edinburgh. ThermaSMART partners span across 5 continents: Europe, Asia, Africa, North America and South America.
ThermaSMART aims to gain a competitive advantage through the exposure of participants to new research environments both in academia and industry which will enable exchange of crucial skills and knowledge and empower their career prospects in this increasingly important area.
The school has already worked with partners from South Africa, Brazil, and Japan on projects to enhance heat-transfer in microelectronic devices. As the only school of Mathematics and Statistics in the network, we have focused in our work on the fundamentals of heat and mass transfer, as proper understanding of these concepts is crucial for the development of novel microelectronic cooling methods.
(opens in a new window)https://thermasmart.eng.ed.ac.uk
Project: Accurate waveforms for extreme- and intermediate-mass-ratio inspirals
Dr Niels Warburton
Funder and Scheme: Science Foundation Ireland, Royal Society Research Grant Scheme
Project Description: My research focuses on modelling the gravitational-wave emission from extreme mass-ratio inspirals (EMRIs) which are sources for the Laser Interferometer Space Antenna (LISA). EMRIs are binary systems where a compact object, such as a stellar mass black hole or neutron star, orbits a massive black hole. Modelling these binaries necessitates solving the relativistic two-body problem and for EMRIs the small mass-ratio can be used to perform a perturbative expansion of the Einstein field equations. These are then solved order-by-order with a combination of analytic and numerical techniques. My current research focuses on both developing new perturbative results and also preparing current results for practical use in gravitational-wave detection and parameter estimation algorithms.