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

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

FaceTouch: Detecting hand-to-face touch with supervised contrastive
learning to assist in tracing infectious disease

Ibrahim, M Lyons, T (24 Aug 2023) http://arxiv.org/abs/2308.12840v1

Unbiased Decisions Reduce Regret: Adversarial Domain Adaptation for the
Bank Loan Problem

Gal, E Singh, S Pacchiano, A Walker, B Lyons, T Foerster, J (15 Aug 2023) http://arxiv.org/abs/2308.08051v1

A structure theorem for streamed information

Salvi, C Diehl, J Lyons, T Preiss, R Reizenstein, J Journal of Algebra (01 Aug 2023)

An Adaptive Algorithm for Rough Differential Equations

Bayer, C Breneis, S Lyons, T (24 Jul 2023) http://arxiv.org/abs/2307.12590v1

Rectifiable paths with polynomial log-signature are straight lines

Friz, P Lyons, T Seigal, A (30 May 2023) http://arxiv.org/abs/2305.19210v1

Dual Bayesian ResNet: A Deep Learning Approach to Heart Murmur Detection

Walker, B Krones, F Kiskin, I Parsons, G Lyons, T Mahdi, A (26 May 2023) http://arxiv.org/abs/2305.16691v1

Hypercontractivity meets random convex hulls: analysis of randomized multivariate cubatures

Hayakawa, S Lyons, T Oberhauser, H Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (17 May 2023)

Sampling-based Nystrom Approximation and Kernel Quadrature

Hayakawa, S Oberhauser, H Lyons, T Proceedings of the 40th International Conference on Machine Learning volume 202 12678-12699 (08 May 2023)

The insertion method to invert the signature of a path

Fermanian, A Chang, J Lyons, T Biau, G (04 Apr 2023)

Optimal stopping via distribution regression: a higher rank signature approach

Horvath, B Lemercier, M Liu, C Lyons, T Salvi, C (04 Apr 2023)

The insertion method to invert the signature of a path

Fermanian, A Chang, J Lyons, T Biau, G (04 Apr 2023) http://arxiv.org/abs/2304.01862v3

Dual Bayesian ResNet: A Deep Learning Approach to Heart Murmur Detection

H. Krones, F Walker, B Mahdi, A Kiskin, I Lyons, T Parsons", G Computing in Cardiology Conference (CinC) (03 Apr 2023)

Positively weighted kernel quadrature via subsampling

Hayakawa, S Oberhauser, H Lyons, T Advances in Neural Information Processing Systems 35 (NeurIPS 2022) (01 Apr 2023)

Learning Dynamic Graph Embeddings with Neural Controlled Differential
Equations

Qin, T Walker, B Lyons, T Yan, H Li, H (22 Feb 2023) http://arxiv.org/abs/2302.11354v1

New Directions in the Applications of Rough Path Theory

Fermanian, A Lyons, T Morrill, J Salvi, C IEEE BITS the Information Theory Magazine volume PP issue 99 1-18 (10 Feb 2023)

New directions in the applications of rough path theory

Fermanian, A Lyons, T Morrill, J Salvi, C (09 Feb 2023) http://arxiv.org/abs/2302.04586v1

Benchmarking optimality of time series classification methods in distinguishing diffusions

Zhang, Z Lu, F Fei, E Lyons, T Kevrekidis, Y Woolf, T (30 Jan 2023)

Sampling-based Nyström Approximation and Kernel Quadrature

Hayakawa, S Oberhauser, H Lyons, T (23 Jan 2023) http://arxiv.org/abs/2301.09517v3

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 volume 185 issue 3-4 705-746 (07 Jan 2023)

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.