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Prof. Terry Lyons FLSW FRSE FRS

Status
Academic Faculty
+44 1865 616611
Contact form
ORCID iD
https://orcid.org/0000-0002-9972-2809
Research groups
  • Machine Learning and Data Science
  • Stochastic Analysis
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Recent books
System control and rough paths Lyons, T Qian, Z (2002)
Research interests

I am the Wallis Professor of Mathematics; I was a founding member (2007) of, and then Director (2011-2015) of, the Oxford Man Institute of Quantitative Finance; I was the Director of the Wales Institute of Mathematical and Computational Sciences (WIMCS; 2008-2011). I came to Oxford in 2000 having previously been Professor of Mathematics at Imperial College London (1993-2000), and before that I held the Colin Maclaurin Chair at Edinburgh (1985-93).

My long-term research interests are all focused on Rough Paths, Stochastic Analysis, and applications - particularly to Finance and more generally to the summarsing of large complex data. That is to say I am interested in developing mathematical tools that can be used to effectively model and describe high dimensional systems that exhibit randomness. This involves me in a wide range of problems from pure mathematical ones to questions of efficient numerical calculation.

Recent publications
Structured Linear CDEs: Maximally Expressive and Parallel-in-Time
Sequence Models
Walker, B Yang, L Cirone, N Salvi, C Lyons, T (23 May 2025) http://arxiv.org/abs/2505.17761v1
Higher order Lipschitz Sandwich theorems
Lyons, T McLeod, A Journal of the London Mathematical Society volume 111 issue 3 (07 Mar 2025)
Signature methods in machine learning
Lyons, T McLeod, A EMS Surveys in Mathematical Sciences (19 Feb 2025)
Transforming CCTV cameras into NO 2 sensors at city scale for adaptive policymaking
Ibrahim, M Lyons, T Scientific Reports volume 15 issue 1 (29 Jan 2025)
Transforming CCTV cameras into NO$_2$ sensors at city scale for adaptive
policymaking
Ibrahim, M Lyons, T (28 Dec 2024)
High-degree cubature on Wiener space through unshuffle expansions
Ferrucci, E Herschell, T Litterer, C Lyons, T (20 Nov 2024)
The Insertion Method to Invert the Signature of a Path
Fermanian, A Chang, J Lyons, T Biau, G Recent Advances in Econometrics and Statistics 575-595 (29 Oct 2024)
Combining hough transform and deep learning approaches to reconstruct ECG signals from printouts
Krones, F Walker, B Lyons, T Mahdi, A (18 Oct 2024)
Deep Signature: Characterization of Large-Scale Molecular Dynamics
Qin, T Zhu, M Li, C Lyons, T Yan, H Li, H (03 Oct 2024)
Investigation of logarithmic signatures for feature extraction and application to marine engine fault diagnosis
Patil, C Theotokatos, G Wu, Y Lyons, T Engineering Applications of Artificial Intelligence volume 138 issue Part A (25 Sep 2024)
Rectifiable paths with polynomial log‐signature are straight lines
Friz, P Lyons, T Seigal, A Bulletin of the London Mathematical Society volume 56 issue 9 2922-2934 (04 Sep 2024)
RoughPy: streaming data is rarely smooth
Morley, S Lyons, T Proceedings of the 23rd Python in Science Conference 320-331 (10 Jul 2024)
Log neural controlled differential equations: the lie brackets make a difference
Walker, B McLeod, A Qin, T Cheng, Y Li, H Lyons, T (08 Jul 2024)
FaceTouch: detecting hand-to-face touch with supervised contrastive learning to assist in tracing infectious diseases
Ibrahim, M Lyons, T PLoS ONE volume 19 issue 6 (13 Jun 2024)
Higher Order Lipschitz Greedy Recombination Interpolation Method
(HOLGRIM)
Lyons, T McLeod, A (05 Jun 2024)
Higher order Lipschitz Sandwich theorems
Lyons, T McLeod, A (10 Apr 2024)
A high order solver for signature kernels
Lemercier, M Lyons, T (02 Apr 2024)
Sig-networks toolkit: signature networks for longitudinal language modelling
Tseriotou, T Chan, R Tsakalidis, A Bilal, I Kochkina, E Lyons, T Liakata, M Proceedings of the 18th Conference of the European Chapter of the Association for Computational Linguistics: System Demonstrations (EACL 2024) 223-237 (22 Mar 2024)
Multimodal deep learning approach to predicting neurological recovery
from coma after cardiac arrest
Krones, F Walker, B Parsons, G Lyons, T Mahdi, A (09 Mar 2024) http://arxiv.org/abs/2403.06027v1
Further details

Stochastic analysis. This is the area of mathematics relating to the rigorous description of high-dimensional systems that have randomness. It is an area of wide-reaching importance. Virtually all areas of applied mathematics today involve considerations of randomness, and a mobile phone would not work without taking advantage of it. Those who provide fixed-rate mortgages have to take full account of it. My interests are in identifying the fundamental language and the basic results that are required to model the interaction between highly oscillatory systems where the usual calculus is inappropriate. If you google ‘Rough Paths’ and ‘Lyons’ you will find further information. My St Flour Lecture notes provide a straightforward technical introduction with all the details put as simply as possible. A more general introduction can be found in my talk/paper to the European Mathematical Society in Stockholm in 2002.
My approach is that of a pure mathematician, but my research has consequences for numerical methods, finance, sound compression and filtering. At the moment I am (speculatively) exploring their usefulness in understanding sudden shocks on dynamical systems, and also trying to understand the implications for geometric measure theory. The focus of my research directed to ‘Rough paths’ can be viewed as a successful approach to understanding certain types of non-rectifiable currents.
I actively look for applications in the mathematics I do, but my experience has led me to believe strongly in the importance of being rigorous in the development of the core mathematical ideas. For me, the word proof is synonymous with the more palatable ‘precise, convincing and detailed explanation’, and I believe it is important, even essential, to find rigorous proofs of the key mathematical intuitions so that mathematics can reliably grow and ideas can be passed on to the next generation.

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London Mathematical Society Good Practice Scheme Athena SWAN Silver Award (ECU Gender Charter) Stonewall Silver Employer 2022

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