Prof. Terry Lyons FLSW FRSE FRS

Status

Academic Faculty

Wallis Professor of Mathematics

Contact form

+44 1865 616611

ORCID iD

https://orcid.org/0000-0002-9972-2809

Research groups

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

PATH SIGNATURES FOR NON-INTRUSIVE LOAD MONITORING

Moore, P Iliant, T Ion, F Wu, Y Lyons, T ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings volume 2022-May 3808-3812 (01 Jan 2022)

Generating Financial Markets With Signatures

Buehler, H Horvath, B Lyons, T Perez Arribas, I Wood, B Risk (09 Jul 2021)

General Signature Kernels

Cass, T Lyons, T Xu, X (01 Jul 2021) http://arxiv.org/abs/2107.00447v1

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)

Modelling paralinguistic properties in conversational speech to detect bipolar disorder and borderline personality disorder

Wang, B Wu, Y Vaci, N Liakata, M Lyons, T Saunders, K Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP) issue 2021 7243-7247 (13 May 2021)

Signature features with the visibility transformation

Wu, Y Ni, H Lyons, T Hudson, R volume 2021 4665-4672 (05 May 2021)

Continuity in κ in SLEκ theory using a constructive method and rough path theory

Beliaev, D Lyons, T Margarint, V Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques volume 57 issue 1 455-468 (01 Feb 2021)

Estimating the probability that a given vector is in the convex hull of
a random sample

Hayakawa, S Lyons, T Oberhauser, H (12 Jan 2021) http://arxiv.org/abs/2101.04250v2

The shifted ODE method for underdamped Langevin MCMC

Foster, J Lyons, T Oberhauser, H (10 Jan 2021) http://arxiv.org/abs/2101.03446v2

Efficient and Accurate Gradients for Neural SDEs

Kidger, P Foster, J Li, X Lyons, T Advances in Neural Information Processing Systems volume 23 18747-18761 (01 Jan 2021)

SK-Tree: a systematic malware detection algorithm on streaming trees via the signature kernel

Cochrane, T Foster, P Chhabra, V Lemercier, M Lyons, T Salvi, C IEEE PROCEEDINGS OF THE 2021 IEEE INTERNATIONAL CONFERENCE ON CYBER SECURITY AND RESILIENCE (IEEE CSR) 35-40 (2021) http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000705054100006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=4fd6f7d59a501f9b8bac2be37914c43e

Neural controlled differential equations for irregular time series

Kidger, P Morrill, J Foster, J Lyons, T Advances in Neural Information Processing Systems 33 (NeurIPS 2020) (10 Dec 2020)

Learning to detect bipolar disorder and borderline personality disorder with language and speech in non-clinical interviews

Wang, B Wu, Y Taylor, N Lyons, T Liakata, M Nevado-Holgado, A Saunders, K Proceedings of the Annual Conference of the International Speech Communication Association, INTERSPEECH 2020 437-441 (16 Nov 2020)

Information extraction from Swedish medical prescriptions with sig-transformer encoder

Pougué Biyong, J Wang, B Lyons, T Nevado-Holgado, A ACL Anthology 41-54 (01 Nov 2020)

Universal approximation with deep narrow networks

Kidger, P Lyons, T Proceedings of the 33rd Annual Conference on Learning Theory (COLT 2020) volume 125 issue 2020 2306-2327 (06 Aug 2020)

Utilisation of the signature method to identify the early onset of sepsis from multivariate physiological time series in critical care monitoring

Morrill, J Kormilitzin, A Nevado-Holgado, A Swaminathan, S Howison, S Lyons, T Critical Care Medicine volume 48 issue 10 e976-e981 (03 Aug 2020)

Deriving information from missing data: implications for mood prediction

Wu, Y Lyons, T Saunders, K (26 Jun 2020) http://arxiv.org/abs/2006.15030v3

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.