# Prof. Terry Lyons FLSW FRSE FRS

Wallis Professor of Mathematics

**Address**

Mathematical Institute

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

*Lyons, T*

*Qian, Z*

*(2002)*

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.

*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)*

*Buehler, H*

*Horvath, B*

*Lyons, T*

*Perez Arribas, I*

*Wood, B*

*Risk*

*(09 Jul 2021)*

*Cass, T*

*Lyons, T*

*Xu, X*

*(01 Jul 2021)*

*http://arxiv.org/abs/2107.00447v1*

*Morrill, J*

*Salvi, C*

*Kidger, P*

*Foster, J*

*7829-7838*

*(01 Jul 2021)*

*Kidger, P*

*Foster, J*

*Li, X*

*Oberhauser, H*

*Lyons, T*

*5453-5463*

*(01 Jul 2021)*

*Kidger, P*

*Chen, R*

*Lyons, T*

*5443-5452*

*(01 Jul 2021)*

*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)*

*Wu, Y*

*Ni, H*

*Lyons, T*

*Hudson, R*

*volume 2021*

*4665-4672*

*(05 May 2021)*

*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)*

a random sample

*Hayakawa, S*

*Lyons, T*

*Oberhauser, H*

*(12 Jan 2021)*

*http://arxiv.org/abs/2101.04250v2*

*Foster, J*

*Lyons, T*

*Oberhauser, H*

*(10 Jan 2021)*

*http://arxiv.org/abs/2101.03446v2*

*Kidger, P*

*Foster, J*

*Li, X*

*Lyons, T*

*Advances in Neural Information Processing Systems*

*volume 23*

*18747-18761*

*(01 Jan 2021)*

*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*

*Kidger, P*

*Morrill, J*

*Foster, J*

*Lyons, T*

*Advances in Neural Information Processing Systems 33 (NeurIPS 2020)*

*(10 Dec 2020)*

*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)*

*Pougué Biyong, J*

*Wang, B*

*Lyons, T*

*Nevado-Holgado, A*

*ACL Anthology*

*41-54*

*(01 Nov 2020)*

*Kidger, P*

*Lyons, T*

*Proceedings of the 33rd Annual Conference on Learning Theory (COLT 2020)*

*volume 125*

*issue 2020*

*2306-2327*

*(06 Aug 2020)*

*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)*

*Wu, Y*

*Lyons, T*

*Saunders, K*

*(26 Jun 2020)*

*http://arxiv.org/abs/2006.15030v3*

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.