I am a reader in the Statistics Laboratory at the University of Cambridge. I am also a fellow of Trinity College. I will hold the Poincare chair at IHP in the 2015-2016 academic year. Previously, I was a post-doc in the Theory Group at Microsoft Research and at MIT. My research interests are in probability, in particular stochastic interface models (random surfaces and SLE), random walk, mixing times for Markov chains, and interacting particle systems.
Lent 2016: Stochastic calculus
Michaelmas 2015: Probability and Measure
Fall of 2014: MIT Math 18.177, a topics course in random planar maps, Liouville quantum gravity, and SLE.
Quantum Loewner Evolution and the Brownian map
- Quantum Loewner Evolution (with S. Sheffield)
- An axiomatic characterization of the Brownian map (with S. Sheffield)
- Liouville quantum gravity and the Brownian map I: the QLE(8/3,0) metric (with S. Sheffield)
Slides on the equivalence of Liouville quantum gravity and the Brownian map.
(Use VLC to play an MKV file)
Mating of Trees / Peanosphere
- Liouville quantum gravity as a mating of trees (with B. Duplantier and S. Sheffield)
- Liouville quantum gravity spheres as matings of finite diameter trees (with S. Sheffield)
- Brownian motion correlation in the peanosphere for k > 8 (with E. Gwynne, N. Holden, and X. Sun)
- Bipolar oriented random planar maps and SLE_12 (with R. Kenyon, S. Sheffield, and D.B. Wilson)
- An almost sure KPZ relation for SLE and Brownian motion (with E. Gwynne and N. Holden)
Slides on the mating of trees
- Imaginary Geometry I: Interacting SLEs (with S. Sheffield)
- Imaginary geometry II: reversibility of SLE_k(rho_1;rho_2) for k in (0,4) (with S. Sheffield)
- Imaginary geometry III: reversibility of SLE_k for k in (4,8) (with S. Sheffield)
- Imaginary geometry IV: interior flow lines, whole plane reversibility, and space filling paths (with S. Sheffield)
Slides on Imaginary Geometry
SLE and CLE
- Hausdorff dimension of the CLE gasket (with N. Sun and D.B. Wilson)
- Intersections of SLE paths: the double and cut point dimension of SLE (with H. Wu)
- Extreme nesting in the conformal loop ensemble (with S.S. Watson and D.B. Wilson)
- The conformal loop ensemble nesting field (with S.S. Watson and D.B. Wilson)
- Almost sure multifractal spectrum of SLE (with E. Gwynne and X. Sun)
- CLE percolations (with S. Sheffield and W. Werner)
- Dimension transformation formula for conformal maps into the complement of an SLE curve (with E. Gwynne and N. Holden)
- CLE(4) and the Gaussian free field (with S. Sheffield)
A space-filling SLE(6) from the top to the bottom of the square, generated using the Gaussian free field. Animation.