Professor of Mathematics, Official Fellow in Mathematics at Exeter College
+44 1865 279629
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Highlighted Publications:
Differential structure and flow equations on rough path space
Bulletin des Sciences Mathematiques
issue 6-7
volume 135
page 695-732
(1 September 2011)
Backward stochastic dynamics on a filtered probability space
Annals of Probability
issue 4
volume 39
page 1422-1448
(1 July 2011)
A study of the navier-stokes equations with the kinematic and navier boundary conditions
Indiana University Mathematics Journal
issue 2
volume 59
page 721-760
(1 December 2010)
Ricci flow on a 3-manifold with positive scalar curvature
Bulletin des Sciences Mathematiques
issue 2
volume 133
page 145-168
(1 March 2009)
An estimate for the vorticity of the Navier-Stokes equation
Comptes Rendus Mathematique
issue 1-2
volume 347
page 89-92
(1 January 2009)
Recent Publications:
Finite dimensional characteristic functions of Brownian rough path
Frontiers of Mathematics in China
issue 4
volume 12
page 859-877
(1 August 2017)
QUASI-SURE EXISTENCE OF GAUSSIAN ROUGH PATHS AND LARGE DEVIATION PRINCIPLES FOR CAPACITIES
OSAKA JOURNAL OF MATHEMATICS
issue 4
volume 53
page 941-970
(October 2016)
Full text available
On an inversion theorem for Stratonovich's signatures of multidimensional diffusion paths
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
issue 1
volume 52
page 429-447
(February 2016)
Full text available
BMO martingales and positive solutions of heat equations
Mathematical Control and Related Fields
issue 3
volume 5
page 453-473
(1 January 2015)
Uniqueness of signature for simple curves
JOURNAL OF FUNCTIONAL ANALYSIS
issue 6
volume 267
page 1778-1806
(15 September 2014)
Full text available
Research Group:
Research Interests:
I am interested in stochastic analysis: diffusion processes, rough path analysis, backward stochastic differential equations and stochastic (partial) differential equations. I am also interested in the Ricci curvature and related partial differential equations, and its applications in the general theory of relativity, quantum fields etc.
Further Details:
Conferences
The second Oxford workshop on probability and its applications will take place in the Mathematical Institute, Andrew Wiles Building, Oxford, from Monday 17 March to Thursday 20 March, 2014. The details about the workshop may be found on the stochastic analysis web page Oxford Probability Workshop.
The infomation about The first Oxford workshop on probability and its applications can be found here.
Teaching:
I am teaching B8.1 Martingales Through Measure Theory, and CDT Foundation course on Measures and Probability Theory, in Michaelmas Term 2015.
Major / Recent Publications:
Recent preprints may be found in arXiv
System Control and Rough Paths (with T. Lyons), Oxford Mathematical Monographs, Clarendon Press, Oxford 2002.