Wallis Professor of Mathematics
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
System control and rough paths
ISBN-10: 0-19-850648-1 (2002)
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 (3 August 2020)
Generating Financial Markets With Signatures
(21 July 2020)
A Data-Driven Market Simulator for Small Data Environments
(21 June 2020)
An optimal polynomial approximation of Brownian motion
SIAM Journal on Numerical Analysis issue 3 volume 58 page 1393-1421 (4 May 2020)
Optimal execution with rough path signatures
SIAM Journal on Financial Mathematics issue 2 volume 11 page 470-493 (27 April 2020)
The signature-based model for early detection of sepsis from electronic health records in the intensive care unit
2019 Computing in Cardiology (CinC) volume 46 (24 February 2020)
Numerical Method for Model-free Pricing of Exotic Derivatives in Discrete Time Using Rough Path Signatures
Applied Mathematical Finance (18 February 2020)
Deep signature transforms
Advances in Neural Information Processing Systems 32 volume 32 page 3082-3092 (10 December 2019)
Using path signatures to predict a diagnosis of Alzheimer’s disease
PLOS ONE issue 9 volume 14 page e0222212-e0222212 (20 September 2019)
Random forest prediction of Alzheimer's disease using pairwise selection from time series data.
PloS one issue 2 volume 14 page e0211558-e0211558 (14 February 2019)
A signature-based machine learning model for distinguishing bipolar disorder and borderline personality disorder
Translational Psychiatry issue 1 volume 8 page 274- (13 December 2018)
Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length (vol 356, pg 720, 2018)
COMPTES RENDUS MATHEMATIQUE issue 10 volume 356 page 987-987 (October 2018) Full text available
Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length
Comptes Rendus Mathématique issue 7 volume 356 page 720-724 (22 May 2018)
A Path Signature Approach to online Arabic Handwriting Recognition
2018 IEEE 2ND INTERNATIONAL WORKSHOP ON ARABIC AND DERIVED SCRIPT ANALYSIS AND RECOGNITION (ASAR) page 135-139 (2018) Full text available
Rotation-free online handwritten character recognition using dyadic path signature features, hanging normalization, and deep neural network
23rd International Conference on Pattern Recognition (ICPR 2016) page 4083-4088 (1 April 2017)
Hyperbolic development and inversion of signature
Journal of Functional Analysis issue 7 volume 272 page 2933-2955 (28 December 2016)
Characteristic functions of measures on geometric rough paths
Annals of Probability issue 6 volume 44 page 4049-4082 (14 November 2016)
Uniform factorial decay estimates for controlled differential equations
Electronic Communications in Probability issue paper no. 94 volume 20 page 1-11 (7 June 2016)
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.
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.