The UCD School of Mathematics and Statistics, SFI’s Centre for Research Training in Foundations of Data Science, the Royal Society SFI University Research Fellowship Scheme, and the UCD College of Science are pleased to offer six undergraduate summer research placements for 2025. The list of available projects is provided below. A stipend of €3,000 will be awarded to each student.
This programme is specifically aimed at undergraduate students entering their final year in autumn 2025, though students in other years may be considered in exceptional cases. The programme is open to students from any institution, not just UCD.
Applicants should submit a single PDF file named <lastname_firstname.pdf>, containing the following documents:
- A cover letter (maximum 1 page) outlining the projects being applied for. It is possible to apply for multiple projects; however, please rank your preferences.
- A CV (maximum 2 pages), also as a single PDF file with the filename <lastname_firstname.pdf>; please see guidance on writing a CV suitable for this programme.
- Academic transcripts (preliminary overviews of grades are acceptable).
Please email your application to (opens in a new window)lars.kuehne+ugsrp@ucd.ie by Thursday, April 10, 2024, at 10:00.
In the event that there are more applicants than available placements, candidates will be ranked based on a weighted average of their GPA, the quality of their CV, and the suitability of their background for specific projects. Successful candidates will be notified in mid to late April. The research projects are expected to last a minimum of 8 weeks, starting in early June, with flexible start dates negotiable with individual supervisors.
Undergraduate research placements offer students an excellent opportunity to develop valuable research skills. Check out reports from previous years and learn about the achievements of some of our alumni!
Creating personalised weather agents
Supervisor: Andrew Parnell
keywords: generative AI, climate change, weather forecasting
In this project the student will create AI agents that take information about a person as well as a weather forecast, and try to personalise the forecast to make it maximally useful to them. A particular challenge will be evaluating the accuracy of these personalised forecasts, and estimating how they might interact with national severe weather warnings which should never be ignored. An extended project would create an Agent that can provide interesting weather facts based on historical data. The ultimate goal will be to retrain an LLM to provide a complete source of weather related data that can absorb new information to provide the latest forecasts in a style that is most relevant to the user.
The successful candidate will have a keen interest in computation and some ability in Python or R. They should have used several Generative AI tools before.
Gravitational waves from precessing black hole binaries
Supervisor: Niels Warburton
keywords: black holes, gravitational waves, perturbation theory
The groundbreaking detection of gravitational waves by the LIGO/Virgo Collaboration (LVC) has generated significant excitement within the physics community, earning the 2017 Nobel Prize in Physics. Even more exciting, this first detection was just the beginning. As the sensitivity of the detectors continues to improve by tuning, the LVC is making ever more groundbreaking discoveries, detecting signals from increasingly distant sources.
The next major advancement in gravitational wave science will come with the launch of the Laser Interferometer Space Antenna (LISA), a flagship L-class mission of the European Space Agency with substantial support from NASA. Just as X-ray, gamma-ray, and radio observations revealed sources previously undetectable by optical telescopes, LISA’s sensitivity to an entirely new gravitational wave frequency band will open the door to a broader range of sources, including extreme mass ratio inspirals (EMRIs), supermassive binary black holes, and exotic objects such as cosmic strings.
The LVC has demonstrated that a hybrid approach is crucial for gravitational wave (GW) science: experimentalists construct the detectors, while theoreticians develop models for the expected waveforms from GW sources. These waveforms play a vital role in the data analysis pipeline, where a matched-filtering approach is employed to extract signals from noisy GW observations. This process critically depends on the availability of accurate waveform models. Without these models, many GW signals would remain undetected, and even those that are identified would be difficult to interpret.
In this project, you will study and develop models for gravitational wave signals from precessing extreme mass ratio inspirals (EMRIs) using an adiabatic approximation to the Einstein field equations and leveraging black hole perturbation theory.
References:
“The evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission”, S. A. Hughes, Phys.Rev.D61:084004 (2000), https://arxiv.org/abs/gr-qc/9910091
“FastEMRIWaveforms: New tools for millihertz gravitational-wave data analysis”, Michael L. Katz, Alvin J.K. Chua, Lorenzo Speri, Niels Warburton, Scott A. Hughes, Phys. Rev. D 104, 064047 (2021), (opens in a new window)https://arxiv.org/abs/2104.04582
The geometry of Lipschitz-free spaces
Supervisor: Richard Smith
Keywords: Lipschitz-free spaces, metric spaces, functional analysis
Lipschitz-free spaces (hereafter free spaces) are Banach spaces that lie on the interface between functional analysis, optimal transport theory and metric geometry. Free spaces (and their duals) are arguably the canonical way to express metric spaces in functional analytic terms, analogously to how compact Hausdorff spaces and measure spaces can be expressed using C(K)-spaces and L_p-spaces, respectively.
While free spaces have been known since [1], they have been studied intensively by members of the functional analysis community ever since the publication of the seminal papers of Godefroy and Kalton (e.g. [2]), and remain a very active research area. One of the reasons for this is that, despite the relative ease with which they can be defined, their structure is complicated and elusive, and many pertinent and ``elementary'' questions concerning their theory remain unanswered.
The aim of this project is to find an explicit or ``closed-form'' expression for the norm of a free space when restricted to two-dimensional subspaces. Time allowing, the problem could be naturally extended to finite-dimensional subspaces. The applicant should be familiar with real analysis (in particular, handling inequalities), metric spaces and preferably (though not necessarily) functional analysis.
More details of the project can be found here.
References:
- F. Arens and J. Eells, On embedding uniform and topological spaces, Pac. J. Math. 6 (1956), 397-403.
- Godefroy and N. J. Kalton, Lipschitz-free Banach spaces, Studia Math. 159 (2003), 121-141.
The Discipline of Noticing: Professional Development for Noticing Students’ Mathematical Thinking
Supervisor: Maria G Meehan
Keywords: noticing, students’ mathematical thinking, professional development
Noticing students’ mathematical thinking is essential for instructors, particularly those who aim to engage in teaching that builds on students’ reasoning. Jacobs et al. (2011) conceptualize noticing students’ mathematical thinking as comprising three interrelated skills:
(a) Attending to student thinking,
(b) Interpreting student thinking, and
(c) Deciding how to respond.
These skills are often required in the moment as instructors navigate students’ questions and responses. Jacobs et al. highlight that deciding how to respond is the most challenging aspect for instructors. However, they note that all three skills can be developed through targeted professional development.
This project explores how Mason’s (2002) Discipline of Noticing can serve as a professional development tool to enhance prospective teachers' or tutors' ability to notice students’ mathematical thinking, with a particular focus on making in-the-moment decisions about how to respond. This project is ideal for undergraduate mathematics students who are prospective teachers or have some experience in tutoring.
The undergraduate researcher will write brief-but-vivid accounts (Mason, 2002) of instructor-student interactions drawn from their teaching or tutoring practice. Through analysis of these accounts, the researcher will characterize the nature of in-the-moment decisions that challenge instructors when responding to student thinking. A literature review will then be conducted to identify evidence-based approaches suitable for the different scenarios documented.
References:
Jacobs, V. R., Lamb, L. L., & Phillip, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, 169-202.
Mason, J. (2002). Researching your own practice: The Discipline of Noticing. London: Routledge Farmer.
Modelling Uncertainty and Sensitivity of an Asteroid Trajectory
Supervisor: James G Herterich
Keywords: asteroid impact, mathematical modelling, uncertainty quantification
Asteroid 2024 YR4 has recently made headlines as a potential "city killer," though with a low probability of impacting Earth. Its trajectory can be modelled using ordinary differential equations, with key sources of uncertainty including its initial position, velocity, and mass. While the Sun’s influence dominates, interactions with other celestial bodies may also affect its path, though their impact is often negligible. This project aims to analyse the uncertainty and sensitivity of an asteroid’s trajectory, particularly determining when an N>2 body approach is necessary.
We will take the following steps:
- Model the motion of an asteroid under an N-body interaction system resembling our Solar System
- Explore key parameters and derive a set of sensitivity equations
- The project is open-ended with questions of the form:
- What range of scenarios exist and can we assign probabilities to them?
- When is an N>2 body approach necessary?
- Besides a direct hit, when might Earth entry take over?
- Other suitable questions may be explored.
The project involves mathematical modeling, scientific computing, and statistical analysis. We aim to work in MATLAB for an environment where packages for numerical solution of differential equations and statistical analysis may be combined. Prior knowledge of MATLAB is not mandatory, but a (mathematical) programming background of some form is necessary. Courses on differential equations, probability, and mechanics are desired.
References:
Desmars, J., Bancelin, D., Hestroffer, D., & Thuillot, W. (2013). Statistical and numerical study of asteroid orbital uncertainty. Astronomy & Astrophysics, 554, A32.
Romano, M. (2020). Orbit propagation and uncertainty modelling for planetary protection compliance verification.
Chodas, P., & Yeomans, D. (1999). Orbit determination and estimation of impact probability for near earth objects. Guidance and Control 1999, Advances in the Astronautical Sciences, Vol. 101, Univelt, San Diego, CA, 1999, pp. 21–40.
Synge, J.L. & Griffith, B.A. (1949). Principles of Mechanics. McGraw-Hill.
Smith, R.C. (2024). Uncertainty Quantification: Theory, Implementation, and Applications. Society for Industrial and Applied Mathematics.
Numerical modelling of moist convection with a day-night cycle
Supervisor: Chris Howland
Keywords: fluid dynamics, numerical methods
Modern numerical studies of atmospheric dynamics rely on complex simulation tools with numerous coupled modeling assumptions. While these models achieve high levels of realism, they can be challenging to interpret physically. This leaves room for simpler models that probe the fundamental dynamics of moist convection, where the condensation of water vapour drives buoyant flows.
One such model is the recently proposed Rainy-Bénard system1, which examines condensation-driven convection in a simplified geometry between two parallel plates. Here, heating from condensation drives rising plumes through a stably stratified ambient fluid.
This project aims to investigate how time-dependent boundary conditions influence moist convection. In "dry" convection (without condensation), flow structures and statistics are known to depend critically on the frequency of boundary temperature oscillations2. In a moist convection system, such oscillations may have an even greater impact, as an evolving convective layer near the bottom boundary could generate both waves and rising plumes in the upper layer.
Using the spectral methods library Dedalus3, this project will perform two-dimensional simulations of the Rainy-Bénard system, incorporating a time-oscillating bottom boundary to mimic the day-night cycle.
The ideal candidate should have basic experience with numerical methods, Python programming, and fluid dynamics. Through this project, they will gain valuable skills in simulation analysis and scientific computing.
References:
1 Vallis et al. (2019) J. Fluid Mech. 862, 162-199
2 Yang et al. (2020) Phys. Rev. Lett., 125, 154502
3 Dedalus Project
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Alumni
2013
Aideen Costello (TCD; Morgan Stanley and First Derivatives)
Julian Eberley (Theoretical Physics, UCD; Software Developer at Citi)
Daniela Mueller (Mathematical Sciences, UCD; PhD UCD 2020)
Benen Harrington (TCD; PhD University of York 2018)
2014
James Fannon (Theoretical Physics, UCD; PhD University of Limerick 2018, Met Eireann)
Andrew Gloster (Theoretical Physics, UCD; MSc Imperial College London; PhD UCD 2018, Arista Networks)
Shane Walsh (Theoretical Physics, UCD; IRC scholar, PhD UCD 2018, Susquehanna International Group)
Adam Keilthy (TCD; PhD University of Oxford 2020; 2-year postdoc at MPIM)
2015
Patrick Doohan (Mathematical Studies, UCD; MSc in Applied Mathematics ICL; PhD ICL 2020)
Maria Jacob (ACM, UCD; Statistical Officer Dept of Transport, UK)
Owen Ward (TCD; PhD candidate at Columbia University, New York)
Paul Beirne (Mathematics, UCD; IRC Scholar, PhD UCD 2020; IMVO, Dublin)
2016
Christopher Kennedy (ACM, UCD; postgraduate student at UCD)
Emily Lewanowski-Breen (Maths and Science Education, UCD; second-level maths and biology teacher at Wesley College, Dublin)
Michael O’Malley (Stats and Maths, UCD; postgraduate student at STOR-i, University of Lancaster, UK)
2017
Adam Ryan (Mathematics, UCD; Analyst for Brown Thomas and Arnotts) - Report
Luke Corcoran (Theoretical Physics, TCD; completed part iii in Cambridge (with distinction), PhD student at Humboldt University Berlin) - Report
Conor McCabe (ACM, UCD; MS Statistical Science at Oxford, Machine Learning Scientist at ASOS) - Report
Joseph Curtis (Statistics, UCD; Core Operations Engineer at Virtu Financial in Dublin) - Report
2018
Cian Jameson (Mathematics, UCD; PhD candidate at UCD) - Report
Chaoyi Lu (Statistics, PhD candidate at UCD) - Report
Khang Ee Pang (Applied & Computational Mathematics, UCD; SFI CRT PhD candidate at UCD) - Report
Oisin Flynn-Connolly (Masters in Mathematics, Orsay, Paris) - Report
Kerry Brooks (Mathematical Science, UCD; Data Analyst at Elephants Don’t Forget) - Report
Kevin Cunningham (Theoretical Physics, UCD; BSc stage 4 student) - Report
Eoin Delaney (Computer Science, UCD; PhD in the Machine Learning and Statistics at Insight UCD) - Report
Shane Gibbons (Mathematics, UCD; Part III at Cambridge; PhD candidate at CWI Amsterdam) - Report
Hou Cheng Lam (Financial Mathematics, UCD; MSc Data & Computational Science UCD) - Report
Jack Lewis (Theoretical Physics, UCD; BSc stage 4 student) - Report
2020
Hugo Dolan (ACM, UCD; BSc stage 3 student) - Report
Piotr Kedziora (BSc Mathematics, NUIG) - Report
Peter Nee (ACM, UCD; BSc stage 4 student) - Report
2021
Padraig Ryan (4th year UCD Maths student; PhD candidate at UCD) - (opens in a new window)Report
Aisling Heanue (ACM, UCD; MSc in Computer Science, UCD) - (opens in a new window)Report
Edwina Aylward (Mathematics, TCD; Part III at Cambridge; PhD candidate in Number Theory at LSGNT, London) - (opens in a new window)Report
Nathan Doyle (ACM, UCD; MSc+PhD candidate in Mathematics of Systems, Warwick) - (opens in a new window)Report
Andrew Fulcher (Mathematics, UCD; PhD candidate at UCD) - (opens in a new window)Report
Ellen O'Carroll (4th year UCD Applied & Computational Mathematics) - Report
PJ Nee (ACM UCD; MASt in Applied Mathematics, Cambridge; PhD candidate at Max Planck Institute for Gravitational Physics (Albert Einstein Institute)) - Report
2022
Adam Keyes (ACM, UCD) and Brian Sheridan (Theoretical Physics, UCD; MSc candidate at ETH Zurich) - Report
Jianan Rui (BSc Mathematics, Operational Research, Statistics and Economics, Warwick; MSc in Statistics, University of Chicago) - Report
Connor O’Reilly (Mathematics, UCD; PhD candidate in Computer Science, Loughborough University) - Report
Shona Brophy (Mathematics, UCD; Part III at Cambridge) - Report
Conor Sievwright (4th year Mathematics, Computer Science and Education, UCD) - Report
2023
Hannah Kerrigan (3rd year Theoretical Physics, TCD)
Brendan Alinquant (4th year Mathematics, UCD) - Report
Jessica DuBerry-Mahon (4th year Theoretical Physics, UCD) - Report
Claudia Schreiber (4th year Mathematics, UCD)
Evan Murphy (4th year Mathematics, UCD) - Report