T.J.Lyons's Home Page

Terry J Lyons

Wallis Professor of Mathematics

Contact Information

Mathematical Institute
UNIVERSITY OF OXFORD
24-29 St Giles', Oxford OX1 3LB
Enquiries: +44 (0) 1865 616600
Direct line: +44 (0) 1865 616611
Fax: +44 (0) 1865 273583
tlyons@maths.ox.ac.uk
http://www.maths.ox.ac.uk

New

The recently published St Flour notes (Differential Equations Driven by Rough Paths: Ecole d'Eté de Probabilités de Saint-Flour XXXIV-2004, Terry J. Lyons, Michael J. Caruana, Thierry Lévy, (Lecture Notes in Mathematics, Springer, ISSN 0721-5363) have a number of errata viewable here.

Research Interests :

Stochastic analysis. My interest relate particularly to the control of non-linear systems driven by rough paths. Prime examples of such systems are provided by stochastic differential equations, and stochastic systems. You can find an broader outline of the area in the home page created some years ago for the contract "Stochastic Analysis and its Applications", a project funded by the European Commission and coordinated by myself.

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 lead 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.

You will get an idea of my research interests by looking at Publications List: and more information about our group and general activities by going to http://sag.maths.ox.ac.uk/samath/ .

I would happily acknowledge the important support received from funding bodies for research.

The following mathematical movies were created by Jessica Gaines and me for my inaugural lecture at Imperial College some years ago:

Brownian motion as Brown might have seen it

movies/br2d.mov (269K Quicktime Movie)

Superbrownian motion

movies/superbm.mov (386K Quicktime Movie)