Status:
Professor of Mathematics, Official Fellow in Mathematics at Exeter College
+44 1865 279629
ORCID iD:
https://orcid.org/
Research groups:
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:
A Quasi-sure Non-degeneracy Property for the Brownian Rough Path
POTENTIAL ANALYSIS
issue 1
volume 51
page 1-21
(July 2019)
Full text available
Parabolic equations with divergence-free drift in space $L_{t}^{l}L_{x}^{q}
Indiana University Mathematics Journal
(1 July 2019)
Fine properties of fractional Brownian motions on Wiener space
Journal of Mathematical Analysis and Applications
issue 1
volume 473
page 141-173
(1 May 2019)
Stochastic partial differential equations driven by space-time fractional noises
STOCHASTICS AND DYNAMICS
issue 2
volume 19
page 1950012-1950012
(April 2019)
Full text available
Parabolic type equations associated with the Dirichlet form on the Sierpinski gasket.
Probability Theory and Related Fields
issue 3
volume 175
page 1063-1098
(January 2019)
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.