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Terry Lyons

Prof. Terry Lyons FLSW FRSE FRS

Status
Academic Faculty
Contact form
+44 1865 616611
ORCID iD
https://orcid.org/0000-0002-9972-2809
Research groups
  • Stochastic Analysis
  • Data Science

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
Benchmarking optimality of time series classification methods in distinguishing diffusions
Zhang, Z Lu, F Lyons, T Kevrekidis, Y Woolf, T Fei, E (30 Jan 2023)
Estimating the probability that a given vector is in the convex hull of a random sample
Hayakawa, S Lyons, T Oberhauser, H Probability Theory and Related Fields (07 Jan 2023)
Identifying psychiatric diagnosis from missing mood data through the use of log-signature features
Wu, Y Goodwin, G Lyons, T Saunders, K PLOS ONE volume 17 issue 11 e0276821-e0276821 (17 Nov 2022)
Signature methods in Machine Learning
Lyons, T McLeod, A
A new definition of rough paths on manifolds
Boutaib, Y Lyons, T Annales de la Faculté des sciences de Toulouse : Mathématiques volume 31 issue 4 1223-1258 (28 Oct 2022)
Hypercontractivity meets random convex hulls: analysis of randomized multivariate cubatures
Hayakawa, S Lyons, T Oberhauser, H (11 Oct 2022)
On the choice of interpolation scheme for neural CDEs
Morrill, J Kidger, P Yang, L Lyons, T Transactions on Machine Learning Research volume 2022 issue 9 (08 Sep 2022)
An Asymptotic Radius of Convergence for the Loewner Equation and Simulation of SLE<inf>κ</inf> Traces via Splitting
Foster, J Lyons, T Margarint, V Journal of Statistical Physics volume 189 issue 2 (03 Sep 2022)
ImageSig: A signature transform for ultra-lightweight image recognition
Ibrahim, M Lyons, T IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops volume 2022-June 3648-3658 (23 Aug 2022)
Higher order kernel mean embeddings to capture filtrations of stochastic processes
Salvi, C Lemercier, M Liu, C Horvath, B Damoulas, T Lyons, T Advances in Neural Information Processing Systems 34 (NeurIPS 2021) volume 20 16635-16647 (01 May 2022)
Path signatures for non-intrusive load monitoring
Moore, P Iliant, T Ion, F Wu, Y Lyons, T ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 3808-3812 (27 Apr 2022)
Developing the Path Signature Methodology and its Application to Landmark-based Human Action Recognition
Yang, W Lyons, T Ni, H Schmid, C Jin, L Stochastic Analysis, Filtering, and Stochastic Optimization (22 Apr 2022) http://arxiv.org/abs/1707.03993v2
Logsig-RNN: a novel network for robust and efficient skeleton-based action recognition
Liao, S Lyons, T Yang, W Schlegel, K Ni, H Proceedings of the 32nd British Machine Vision Conference (25 Nov 2021)
Areas of areas generate the shuffle algebra
Diehl, J Lyons, T Preiß, R Reizenstein, J (08 Jul 2021) http://arxiv.org/abs/2002.02338v2
Neural rough differential equations for long time series
Morrill, J Salvi, C Kidger, P Foster, J 7829-7838 (01 Jul 2021)
Neural SDEs as infinite-dimensional GANs
Kidger, P Foster, J Li, X Oberhauser, H Lyons, T 5453-5463 (01 Jul 2021)
"Hey, that's not an ODE": faster ODE adjoints with 12 lines of code
Kidger, P Chen, R Lyons, T 5443-5452 (01 Jul 2021)
General Signature Kernels
Cass, T Lyons, T Xu, X (01 Jul 2021)
Neural Controlled Differential Equations for Online Prediction Tasks
Morrill, J Kidger, P Yang, L Lyons, T (21 Jun 2021)
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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