Hamilton Trust Summer Mathematics Research Internship

Coordinator

The current coordinator is Prof. Marvin Anas Hahn, who can be reached by email at HAHNMA@tcd.ie.

General Information

The School of Mathematics has resources to support a modest internship programme in the summer. The programme takes place over a period of six week, culminating in a poster session for participants display their research. Maths, TP, and Joint Honours Maths undergraduates from years two, three, and four as well as any visiting Exchange students can apply for this programme. It is envisaged that for the whole period of the programme interns will work on a research project in maths under the supervision of a member of staff (the main condition is that the project has mathematical content; supervision by TCD staff members outside School of Maths is in principle permitted (e.g. School of Computer Science and Statistics, or School of Physics), or be designed with a real life application as an end goal.

Internship Information Session

The information session about the internship will be held via Zoom on 16 February 2023 at 6pm. A video recording of the previous internship information session, held via Zoom, can be found here. Please contact Prof. Marvin Anas Hahn at HAHNMA@tcd.ie for a link to the Zoom session.

Financial Support

Due to a generous gift from the Hamilton Trust, the School of Mathematics is able to offer moderate financial support of €900/€1575/€2025 euro for 1/2/3 person project.

The Internship Period

The internship period is tentatively planned to take place between the weeks of 15 May 2023 to 19 June 2023. It is expected that during the term of an internship a weekly seminar will take place, which all interns are required to attend. Moreover, each intern will give a seminar talk introducing the topic of or giving a status report on their project. Students should meet with their research supervisors regularly according to a schedule arranged between students and supervisors. Each individual student must give a presentation during one of the seminars. There will be a poster session at the end of the internship period on Late June 2023.

Application process

It is believed that research internships are of potential benefit to all students, not just those with the strongest exam record, and the selection process will not rely on exam marks, however the quality of actual proposed projects will be taken into account when making the final decision on funding. Typically students should inquire directly to potential supervisors to see if they have a project they would consider supervising.

Once they agreed on the topic of the project, they should register their interest through the online application form in which the applicant(s) will be provided an avenue to upload a PDF file with a short (up to one page using font size 11) description of proposed research project.

Please apply by 5pm on Friday 10 March 2023. Late applications will not be considered. Applications will be processed and selections will be made as soon as possible thereafter by the selection committee.

Sample Proposal

Potential applicants can view a sample proposal to get a sense of the structure a one-page proposal should take for the summer internship.

Publicity Consent

It is important for the Hamilton Trust, Trinity College Dublin, and The School of Mathematics to publicize the running of and output from the Hamilton Trust Summer Internship Programme. This entails the possible use of names of interns and as well as photographs of participants engaging in internship activities.

If your project is selected to run this summer, then it will be necessary that each member of your group fills out and signs a form indicated whether or not their name and/or image may be used when publicizing activities related to the internship.

You have the right to refuse consent to use your image or name in publicizing the activities of the internship. Furthermore, if you give consent in this form, you may later revoke that consent.

You will be asked to give/refuse consent to the use of your name and image for publicity of the internship when applying.

In the event of Covid-19

Due to the pandemic, we have in previous years conducted the internship virtually. We anticipate that the internship will take place live and in-person this year, but should there be a change in the situation necessitating reduced in-person contact, the internship will shift to being virtual, as in previous years.

2023

• An Analytical Investigation of the Ising Model, Supervisor: Dr. Stefan Sint
• Price Forecasting Using Hierarchical Hidden Markov Models, Supervisor: Dr. Jason Wyse
• Theory of Quantum Sensing in Non-Markovian Environments, Supervisor: Dr. Paul Eastham
• Free Loop Spaces and Cochain Complexes on S^2, Supervisor: Dr. Florian Naef
• The Combinatorics of Pruned Hurwitz Numbers, Supervisor: Dr. Marvin Anas Hahn
• Investigation of the mathematical viability of on-the-fly optimisation of Hubbard-corrected approximate density-functional theory, Supervisor: Dr. David O'Regan
• Monte Carlo Propagation of Effective Hamiltonian Models of Two-Sublattice Ferrimagnets for the Construction of Magnetic Phase Diagrams and the Simulation of Hysteresis and Torque Curves , Supervisor: Dr. Plamen Stamenov
• Steganographic Attacks on Machine Learning Models, Supervisor: Dr. Alessio Benavoli
• Machine-learning non-interacting kinetic-energy functionals, Supervisor: Dr. Stefano Sanvito
• Modelling Strongly Interacting Many-Particle Quantum Systems using Physically Constrained Artificial Neural Networks, Supervisor: Dr. Chaolun Wu
• Testing theories of gravity using pulsars, Supervisor: Dr. Evan Keane
• Effects of spatiotemporal resolution on ensemble spread, Supervisor: Dr. Kirk Soodhalter
• Counting McKay quivers for finite subgroups of SO(3), Supervisor: Dr. Sergey Mozgovoy
• Computable Model Theory and Higher Recursion Theory, Supervisor: Dr. Ó Dúnlaing

2022

• Gödel's Theorems After Gödel , Supervisor: Dr. Colm Ó Dúnlaing
• Incorporating Temporal Dependence to Counterfactuals in Reinforcement Learning, Supervisor: Dr. Ivana Dusparic
• Kernel Density Estimation, Supervisor: Dr. Athanasios Georgiadis
• An Investigation into Modular Forms and their Applications, Supervisor: Nicolas Mascot
• t-Distributed Stochastic Neighbourhood Embedding, Supervisor: Dr. Jason Wyse
• Studying Failure with Ideas from Chaos, Supervisor: Dr Stefan Hutzler
• Periods and families of curves, Supervisor: Jack Kelly
• Investigating the suitability of the Big Five model as a basis for Personality., Supervisor: Dr. Arthur White
• Investigating the Gamma Function, Supervisor: Prof. Ruth Britto
• An Investigation of Markov Chain Monte Carlo Methods, Supervisor: Professor Stefan Sint
• Random Fields on Manifolds, Supervisor: Athanasios Georgiadis
• Allocating electricity supply in TCD using Decentralised Autonomous Organisations, Supervisor: Prof. Donal O’Mahony
• On the unsuitability of classical asymptotic results of estimators in modern big data applications, Supervisor: Dr. Jason Wyse
• T-Tbar Multi-parameter Deformations, Supervisor: Professor Sergey Frolov
• Black Holes: The Attractor Mechanism and The Weak Gravity Conjecture, Supervisor: Prof. Jan Manschot

2021

• Quantum Mechanical Properties of Graphene, Supervisor: Dr. Stephen Power
• Solving large sparse linear systems using Krylov subspaces, Supervisor: Kirk M. Soodhalter and Simon Wilson
• Machine Learning as a tool to automatically extract information from scientific publications, Supervisor: Stefano Sanvito
• Modelling the Spread of Covid-19 in Ireland, Supervisor: Athanasios Georgiadis
• Gravitational Phenomena in the Dual Quantum Theory Description, Supervisor: Prof. Manuela Kulaxizi
• Thermalisation and Quantum Scarring in Spin Chain Models, Supervisor: Prof. Tristan McLoughlin
• Classification of Finite Rings, Supervisor: Prof. Nicolas Mascot
• “Investigating the Relationship Between Relative Inequality in Early Life and Incidence of Dementia in Later Life”, Supervisor: Dominic Trepel
• Modelling Spatial Cox Processes on the Sphere using R, Supervisor: Dr. Simon Wilson
• Decoherence of Electro-Nuclear Spin Qubits with Machine Learning, Supervisor: Prof. Alessandro Lunghi
• Detecting Machine Generated Text with Neural Networks, Supervisor: Jason Wyse
• Low Regularity Lyapunov Stability Theory for Autonomous Systems, Supervisor: Prof. John Stalker
• The Yang-Mills Equations over Riemann Surfaces, Supervisor: Florian Naef
• Simulation of Flow-field in Non-linear Rotational Water Waves with Random Free Surface, Supervisor: Prof. Biswajit Basu and Prof. Kirk Soodhalter
• A Modern Maximum Likelihood Theory for High Dimensional Logistic Regression", Supervisor: Jason Wyse

2020

• Cluster Algebras and Applications, Supervisor: Dr Marius de Leeuw
• Feynman Integrals and Hypergeometric Functions, Supervisor: Ruth Britto
• Mathematical properties and applications of the Kortegweg-De Vries equation, Supervisor: Jan Manschot
• Investigating and implementing symbolic integration algorithms, Supervisor: Prof. Mascot
• The Positive Mass Theorem for Graphs and Related Cases, Supervisor: John Stalker
• Examining the Benefits of Semi-Supervised Learning over Supervised Learning, Supervisor: Dr. Arthur White
• A Bayesian Investigation into Lifestyle Modifications and Dementia, Supervisor: Prof. Dominic Trepel
• Using Neural Networks to Analyse Meteor Data, Supervisor: Professor Rozenn Dahyot
• Anomalous dimensions and Random Matrix Theory, Supervisor: Tristan McLoughlin
• Modelling the Spread of Disease through the Collisions of Particles, Supervisor: Prof. Kirk Soodhalter
• Monte Carlo Estimates of Matrix Determinants, Supervisor: Mike Peardon
• Constructing a UTP theory for the C programming language, Supervisor: Dr. Andrew Butterfield
• A Study of Non-Collapsible Contractible Spaces , Supervisor: Colm Ó Dúnlaing
• From the Eightfold Way to Quark Models: The Role of Symmetries in Elementary Particle Physics, Supervisor: Sinéad Ryan
• C code for Topological Data Analysis (TDA), Supervisor: Colm Ó Dúnlaing
• A study on the properties of fractal electronic quantum systems, Supervisor: Dr. Stephen Power

2019

• Nanosheet Networks, Supervisor: Mauro Ferreira
• The study of phase transitions in 2D Potts model, Supervisor: Dr. Marina Krstic Marinkovic
• Analysing multivariate categorical data using latent class analysis in the context of a longitudinal aging survey requiring population re-weighting, Supervisor: Arthur White
• Geodesic Motion of Deformed Manifolds, Supervisor: Tristan McLoughlin
• Investigation of the importance of the order of updates in Monte Carlo computations of a quantum field, Supervisor: Mike Peardon
• Image Restoration With Töplitz-Structure Blurring Models, Supervisor: Prof. Kirk M. Soodhalter
• Counting short exact sequences of modules over K[x], Supervisor: Professor Sergey Mozgovoy
• Model selection with gamma tilted positive stable frailty models, Supervisor: Dr. Bernardo Nipoti
• Bayesian clustering analysis: combining evidence from different studies, Supervisor: Bernardo Nipoti
• Image Regularization using Neural Networks, Supervisor: Prof. Kirk M. Soodhalter
• Flare diagnosis in auto-immune diseases, Supervisor: Arthur White
• Mathematics of Machine Learning and its Applications in Social Science Research, Supervisor: Sinéad M. Ryan
• Strong exotic matter: QCD through numerical simulations, Supervisor: Sinéad M. Ryan
• Mathematical insights on transient population dynamics: response of plant populations to ecological disturbance in a changing world, Supervisor: Kirk M. Soodhalter and Ruth Kelly
• Interactively Prototyping Properties of Rigid Bodies for Physically-based Animation, Supervisor: John Dingliana
• The role of facultative scavenging on food web dynamics, Supervisor: Prof Andrew Jackson (Ecology)
• Building UTP theories with a bespoke theorem prover, Supervisor: Dr. Andrew Butterfield
• Implementing a Convex Hull Algorithm to 4-Dimensional Datasets, Supervisor: Jose Refojo
• Quantum states and partition functions, Supervisor: Jan Manschot
• Monte Carlo estimates of Matrix Determinants, Supervisor: Mike Peardon
• Interpolation with missing endpoints, Supervisor: John Stalker
• Understanding Lie theory and its application in the study of Skew Howe Duality and Young diagrams., Supervisor: Prof. Miriam Logan
• A twisted Richardson-Gaudin model, Supervisor: Tristan McLoughlin

2018

• Development of mathematical techniques to usef EMG measurements to diagnose Motor Neuron Disease, Supervisor: Kirk M. Soodhalter and Bahman Nasseroleslami
• Multivariate Analysis of Vasculitis Biomarker Values in and out of Flare Periods, Supervisor: Dr Jason Wyse
• Modelling Rare Disease Rates using Methods Built on Generalised Linear Models, Supervisor: Dr Jason Wyse
• An Investigation of Extrapolation of Survival Data in the Context of Pharmacoeconomic Evaluation, Supervisor: Arthur White
• Bayesian Latent Class Analysis with Distal outcomes, Supervisor: Arthur White
• Positive Maps, Supervisor: Richard Timoney
• Arbitrary Precision Computation of Modular Functions, Supervisor: Caelen Feller
• Hilbert Schemes of Points, Supervisor: Vladimir Dotsenko
• An investigation into the nature of modern solutions to the problem of sphere packing: including modular forms magic auxiliary functions and their fourier transforms., Supervisor: Jan Manschot
• Non-planar anomalous dimensions in N = 4 super-Yang-Mills, Supervisor: Tristan Mcloughlin
• Entanglement Entropy in the Heisenberg Spin Chain, Supervisor: Dr. Marius de Leeuw
• Path Integrals in Quantum Mechanics, Supervisor: Prof. Stefan Sint
• The Firewall, Supervisor: Prof Jan Manschot
• A Mathematician’s Guide to Meditative Visualisation, Supervisor: Elizabeth Oldham