Post-Doctoral Research Assistant
University of Oxford,
24-29 St Giles',
Only a few minutes walk from Edinburgh into the Pentland hills...
(Follow the link and zoom in for a change of perspective.)
I am interested in many things geometric; in particular, analysis on metric spaces, geometric group theory, hyperbolic groups ...
Papers and preprints
- Existence of quasi-arcs, Proc. Amer. Math. Soc. 136 (2008), no. 11, 3975--3981.
- Spaces with conformal dimension greater than one, Duke Math. J. Volume 153, Number 2 (2010), 211-227.
- Conformal dimension: theory and application, with
University Lecture Series, AMS 2010. More information.
- Assouad dimension of self-affine carpets, Conform. Geom. Dyn. 15 (2011), 177-187.
pdf journal version.
- You can draw your own self-affine (Bedford-McMullen) carpets
- Your browser will ask you to accept a not very impressive security certificate. If you decline
it should still run, but you won't be able to save pictures. Also, the applet uses Java 1.6.
(Test your java version here.)
- Conformal dimension and random groups, Geom. Funct. Anal. Volume 22, Number 1 (2012), 213-239.
- Differentiable structures on metric measure spaces: A Primer, with
B. Kleiner, preprint. arxiv:1108.1324
- Quasi-hyperbolic planes in relatively hyperbolic groups, with
A. Sisto, preprint. arxiv:1111.2499
- Modulus and Poincaré inequalities on non-self-similar Sierpinski carpets, with
J. T. Tyson and
K. Wildrick, Geom. Funct. Anal., to appear. arxiv:1201.3548
- Embedding relatively hyperbolic groups in products of trees, with
A. Sisto, Alg. Geom. Top, to appear. arxiv:1207.3008
- Quasi-circles through prescribed points, Indiana U. Math. J., to appear. arxiv:1210.5119
Expository notes (not for publication)
At the University of Oxford, I am primarily working with
and other members in the topology group.
Before coming here, I was a J.L.Doob research assistant professor at the
University of Illinois from 2008 until the end of 2010.
I was a graduate student at the University
of Michigan (2003-2008), where I worked with Bruce Kleiner. I also spent most of 2006-8 visiting the mathematics department at Yale.
Before that, I was an undergraduate at the University of