Terence "Terry" John Lyons is a British mathematician, specializing in

stochastic analysis Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. This field was created an ...

. Lyons, previously the Wallis Professor of Mathematics, is a fellow of St Anne's College, Oxford and a Faculty Fellow at The Alan Turing Institute. He was the director of the

Oxford-Man Institute The Oxford-Man Institute of Quantitative Finance is an interdisciplinary research institute of the University of Oxford, England. The institute was co-founded in June 2007 with Man Group plc. It brings together faculty, post-docs and students ...

from 2011 to 2015 and the president of the London Mathematical Society from 2013 to 2015. His mathematical contributions have been to

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speakin ...

, harmonic analysis, the

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods ...

stochastic differential equations A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used to model various phenomena such as stock pr ...

, and

quantitative finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require ...

. In particular he developed what is now known as the theory of

rough path In stochastic analysis, a rough path is a generalization of the notion of smooth path allowing to construct a robust solution theory for controlled differential equations driven by classically irregular signals, for example a Wiener process. The the ...

s. Together with Patrick Kidger he proved a universal approximation theorem for neural networks of arbitrary depth.

Education

Lyons obtained his

B.A. Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four yea ...

Trinity College, Cambridge Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge or Oxford. ...

and his D.Phil at the

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

Career

Lyons has held positions at

UCLA The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California ...

Imperial College London Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...

, the

University of Edinburgh The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 15 ...

and since 2000 has been Wallis Professor of Mathematics at the

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

. He was the Director of the

at the University of Oxford from 15 June 2011 to 15 December 2015. He also held a number of visiting positions in Europe and North America. Together with Zhongmin Qian he wrote the monograph ''System Control and Rough Paths'', and together with Michael J. Caruana and Thierry Lévy the book ''Differential Equations Driven by Rough Paths''.

Honours and awards

In 1985 he was awarded the

Rollo Davidson Prize The Rollo Davidson Prize is a prize awarded annually to early-career probabilists by the Rollo Davidson trustees. It is named after English mathematician Rollo Davidson (1944–1970). Rollo Davidson Trust In 1970, Rollo Davidson, a Fellow-el ...

. In 1986 he was awarded the

Whitehead Prize The Whitehead Prize is awarded yearly by the London Mathematical Society to multiple mathematicians working in the United Kingdom who are at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whiteh ...

of the London Mathematical Society. In 2000 he was awarded the Pólya Prize of the London Mathematical Society. He was elected a fellow of the Royal Society of Edinburgh in 1988, and elected a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathemat ...

in 2002; he was made a fellow of the

Institute of Mathematical Statistics The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts o ...

, in 2005 and a fellow of the

Learned Society of Wales The Learned Society of Wales ( Welsh: Cymdeithas Ddysgedig Cymru) is a learned society and charity that exists to "celebrate, recognise, preserve, protect and encourage excellence in all of the scholarly disciplines", and to serve the Welsh natio ...

in 2011. In 2013, he was elected president of the London Mathematical Society. In 2007 he was awarded a Doctor Honoris Causa from the

University of Toulouse The University of Toulouse (french: Université de Toulouse) was a university in the French city of Toulouse that was established by papal bull in 1229, making it one of the earliest universities to emerge in Europe. Suppressed during the Frenc ...

, he was made an Honorary Fellow of Aberystwyth University in 2010 and Cardiff University in 2012. In 2017 he was awarded an honorary Doctor of Mathematics from the

University of Waterloo The University of Waterloo (UWaterloo, UW, or Waterloo) is a public research university with a main campus in Waterloo, Ontario, Canada. The main campus is on of land adjacent to "Uptown" Waterloo and Waterloo Park. The university also operates ...

References

{{DEFAULTSORT:Lyons, Terry Living people 20th-century British mathematicians 21st-century British mathematicians Probability theorists Wallis Professors of Mathematics Fellows of St Anne's College, Oxford Academics of the University of Edinburgh Fellows of the Royal Society 1953 births