Personal Website:
+44 1865 615175
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Highlighted Publications:
Invariance principle for the random conductance model
Probability Theory and Related Fields
issue 3-4
volume 156
page 535-580
(1 August 2013)
Convergence of mixing times for sequences of random walks on finite graphs
Electronic Journal of Probability
volume 17
page 1-32
(31 January 2012)
Asymptotics for functions associated with heat flow on the Sierpinski carpet
Canadian Journal of Mathematics. Journal Canadien de Mathématiques
volume 63
page 153-180
(2011)
Diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice
Communications in Mathematical Physics
volume 295
page 29-69
(2010)
Uniqueness for the signature of a path of bounded variation and the reduced path group
Annals of Mathematics. Second Series
volume 171
page 109-167
(2010)
Recent Publications:
A stochastic partial differential equation model for the pricing of mortgage-backed securities
Stochastic Processes and their Applications
issue 11
volume 128
page 3778-3806
(1 November 2018)
Heat kernel estimates for FIN processes associated with resistance forms
Stochastic Processes and their Applications
(5 September 2018)
Degenerate limits for one-parameter families of non-fixed point diffusions on fractals
Journal of Fractal Geometry
(26 July 2018)
How nanoscale protein interactions determine the mesoscale dynamic organisation of bacterial outer membrane proteins.
Nature communications
issue 1
volume 9
page 2846-
(20 July 2018)
Existence and space-time regularity for stochastic heat equations on p.c.f. fractals
Electronic Journal of Probability
(27 February 2018)
Research Interests:
I am a University Lecturer in the Mathematical Institute. I obtained my PhD from the University of Cambridge and held post-doctoral positions at the University of Cambridge and the University of California, San Diego. I previously held academic positions at the Universities of Edinburgh and Bristol before moving to Oxford in 2000.
My research interests are in the area of probability, stochastic processes, mathematical finance and fractals. For further information see my webpage.