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 ...

. Lyons, previously the

Wallis Professor of Mathematics The Wallis Professorship of Mathematics is a chair in the Mathematical Institute of the University of Oxford. It was established in 1969 in honour of John Wallis, who was Savilian Professor of Geometry at Oxford from 1649 to 1703. List of Wallis ...

, is a fellow of

St Anne's College, Oxford St Anne's College is a constituent college of the University of Oxford in England. It was founded in 1879 and gained full college status in 1959. Originally a women's college, it has admitted men since 1979. It has some 450 undergraduate and ...

and a Faculty Fellow at

The Alan Turing Institute The Alan Turing Institute is the United Kingdom's national institute for data science and artificial intelligence, founded in 2015 and largely funded by the UK government. It is named after Alan Turing, the British mathematician and computing p ...

. He was the director of the Oxford-Man Institute from 2011 to 2015 and the president of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

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 (probability theory), 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 ...

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an e ...

, 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 th ...

of stochastic differential equations, and quantitative finance. In particular he developed what is now known as the theory of rough paths. Together with Patrick Kidger he proved a universal approximation theorem for neural networks of arbitrary depth.

Education

Lyons obtained his B.A. at

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 A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

at the

University of Oxford The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the world's second-oldest university in contin ...

Career

Lyons has held positions at

UCLA The University of California, Los Angeles (UCLA) is a public university, public Land-grant university, land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a Normal school, teachers colle ...

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 ...

, 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

at the

. He was the Director of the Oxford-Man Institute 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. Whitehea ...

of the

. In 2000 he was awarded the Pólya Prize of the

. 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 mathematic ...

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 ...

, 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

. 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 Aberystwyth University ( cy, Prifysgol Aberystwyth) is a Public university, public Research university, research university in Aberystwyth, Wales. Aberystwyth was a founding member institution of the former federal University of Wales. The universi ...

in 2010 and

Cardiff University , latin_name = , image_name = Shield of the University of Cardiff.svg , image_size = 150px , caption = Coat of arms of Cardiff University , motto = cy, Gwirionedd, Undod a Chytgord , mottoeng = Truth, Unity and Concord , established = 1 ...

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