Research Interests
Analysis of PDEs
I am interested in techniques used to prove various properties of solutions to differential equations, especially those with physical relevance. Examples of equations I have studied include the Schrödinger equation, the Manakov system, and the Landau–Lifshitz–Gilbert equation.
Dynamical Systems
Dynamical systems, either representing some process, for instance, interacting particle systems or the objects of statistical mechanics, or sometimes as a discretisation of a differential equation, e.g., the output of a numerical scheme. Techniques from dynamical systems are closely related to the study of PDEs.
Probability
I am primarily interested in systems that operate under the influence of randomness. This randomness can be viewed as accounting for uncertainty, i.e., incomplete knowledge, or as an intrinsic property of the system. Either way, it introduces new mathematical challenges to the study of the problem, especially when the noise is very irregular.
A Short CV
Education
PhD Mathematics (09/21 - 10/25) University of Edinburgh, MAC-MIGS CDT.
Title: Resonance Analysis for Dispersive Equations: Numerical Schemes and Normal Forms. Supervised by Professor Yvain Bruned.
MSc Mathematics (09/19 - 10/20) University of Warwick.
Title: Metrics Between Probability Distributions on Countable Products of Polish Spaces. Supervised by Professor Robert MacKay.
BSc Mathematics (09/16 - 10/19) University of Manchester.
Talks
Summer School (06/24) 13th Cornell Probability Summer School
Title: Low Regularity Numerical Schemes for SPDE
Conference Speaker (05/24) Recontre ANR, Laboratoire de Mathematiques de Bretagne Atlantique
Title: Resonance based numerical schemes for Dispersive SPDE
Conference Speaker (06/23) Hopf Algebras, Operads, Deformations for Singular Dynamics, Institut Elie Cartan de Lorraine
Title: Low Regularity Numerical Schemes for SPDE
Conference Speaker (06/23) GdR TRAG, Université PSL
Title: Low Regularity Numerical Schemes for SPDE
Summer School (06/23) 51st St-Flour Summer School in Probability
Title: Low Regularity Numerical Schemes for SPDE
Conference Speaker (12/22) Oxford-Berlin Young Researchers' Meeting on Applied Stochastic Analysis
Title: Dobrushin and Steif Metrics are Equal
Detailed CV
Research
Publications
Armstrong-Goodall, J.A., MacKay, R.S.
Dobrushin and Steif Metrics are Equal. J Theor Probab 38, 66 (2025).
doi:10.1007/s10959-025-01438-5
Preprints
Armstrong-Goodall, J.A., Bruned, Y.
Birkhoff Normal Forms via Decorated Trees
arXiv:2505.04547
Armstrong-Goodall, J.A., Bruned, Y.
Low Regularity Symplectic Schemes for SNLS.
arXiv.2410.22359
Armstrong-Goodall, J.A., Bruned, Y.
Resonance Based Schemes for SPDE.
arXiv:2312.16690
Theses
Author: J Armstrong-Goodall, Supervisor: Professor RS MacKay,
Metrics on the Space of Distribtutions on the Product of Countable Polish Spaces
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Reports
Authors: J Armstrong-Goodall,A Istratuca, RA Lascu, Supervisor: B Leimkuhler
Quantum Annealing Dynamics
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Biography
About Me
I was born in Huddersfield, a town in the North of England, smack bang between Leeds and Manchester. I have also spent time living in Perth, Western Australia. In Perth, I trained as a chef, but I preferred reading about science and philosophy. Later, I decided to retrain and study mathematics. I obtained an undergraduate degree in maths at the University of Manchester in 2019. I wrote my master's thesis under the supervision of Professor Robert MacKay at the University of Warwick, focusing on proving a duality theorem for a metric on the space of distributions over configurations of interacting particle systems, and graduated in 2020. In 2021, I joined the MAC-MIGS CDT in the Maxwell Institute in Edinburgh as a PhD student. I worked with Yvain Bruned on low-regularity numerical schemes for SPDEs and normal form reductions for Hamiltonian PDEs. I am currently a Wen-Tsun Wu Assistant Professor at Shanghai Jiao Tong University. In my free time, I practice calisthenics and still enjoy cooking.
