## Status:

Wallis Professor of Mathematics

+44 1865 616611

## ORCID iD:

https://orcid.org/0000-0002-9972-2809## Research groups:

## Address

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

## Recent Books:

System control and rough paths

ISBN-10: 0-19-850648-1
(2002)

## Recent Publications:

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

Proceedings of the 2021 IEEE International Conference on Cyber Security and Resilience, CSR 2021
page 35-40
(26 July 2021)

Generating Financial Markets With Signatures

Risk
(9 July 2021)

General Signature Kernels

(1 July 2021)
Full text available

Neural SDEs as infinite-dimensional GANs

volume abs/2102.03657
page 5453-5463
(1 July 2021)

Neural rough differential equations for long time series

CoRR
volume abs/2009.08295
page 7829-7838
(1 July 2021)

"Hey, that's not an ODE": Faster ODE Adjoints via Seminorms

CoRR
volume abs/2009.09457
(18 July 2021)

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

Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
issue 2021
page 7243-7247
(13 May 2021)

Signature features with the visibility transformation

2020 25th International Conference on Pattern Recognition (ICPR)
volume 2021
page 4665-4672
(5 May 2021)

Continuity in $κ$ in $SLE_κ$ theory using a constructive
method and Rough Path Theory

L'Institut Henri Poincare, Annales B: Probabilites et Statistiques

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

(12 January 2021)
Full text available

The shifted ODE method for underdamped Langevin MCMC

(10 January 2021)
Full text available

Neural controlled differential equations for irregular time series

Advances in Neural Information Processing Systems 33 (NeurIPS 2020)
(10 December 2020)

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

Proceedings of the Annual Conference of the International Speech Communication Association, INTERSPEECH 2020
page 437-441
(16 November 2020)

Information extraction from Swedish medical prescriptions with sig-transformer encoder

ACL Anthology
page 41-54
(1 November 2020)

Universal approximation with deep narrow networks

Proceedings of the 33rd Annual Conference on Learning Theory (COLT 2020)
issue 2020
volume 125
page 2306-2327
(6 August 2020)

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

Critical Care Medicine
issue 10
volume 48
page e976-e981
(3 August 2020)

Deriving information from missing data: implications for mood prediction

(26 June 2020)
Full text available

A Data-Driven Market Simulator for Small Data Environments

(21 June 2020)

Anomaly detection on streamed data

(5 June 2020)
Full text available

## 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.

## 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.