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Math(s)
at
Oxford

John Mackay

Post-Doctoral Research Assistant

Mathematical Institute,
University of Oxford,
24-29 St Giles',
Oxford,
OX1 3LB,
UK.

Only a few minutes walk from Edinburgh into the Pentland hills...

(Follow the link and zoom in for a change of perspective.)

Research

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. arxiv:0708.0824 pdf journal version
• Spaces with conformal dimension greater than one, Duke Math. J. Volume 153, Number 2 (2010), 211-227. arxiv:0711.0417 pdf journal version
• Conformal dimension: theory and application, with J.T. Tyson, University Lecture Series, AMS 2010. More information.
• Assouad dimension of self-affine carpets, Conform. Geom. Dyn. 15 (2011), 177-187. arxiv:1003.0930 pdf journal version.
  • You can draw your own self-affine (Bedford-McMullen) carpets here.
  • 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. arxiv:1011.3167 pdf journal version
• Differentiable structures on metric measure spaces: A Primer, with B. Kleiner, preprint. arxiv:1108.1324 pdf
• Quasi-hyperbolic planes in relatively hyperbolic groups, with A. Sisto, preprint. arxiv:1111.2499 pdf
• 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 pdf
• Embedding relatively hyperbolic groups in products of trees, with A. Sisto, preprint. arxiv:1207.3008 pdf
• Quasi-circles through prescribed points, preprint. arxiv:1210.5119 pdf

Expository notes (not for publication)

• Cheeger differentiation, after Cheeger and Keith. Summary written for 2008 Summer School on Quasiconformal analysis and boundaries of hyperbolic groups at Indiana University. pdf (See the improved note above written with Bruce Kleiner.)
• The Heisenberg group does not admit a bi-Lipschitz embedding into L¹, after Cheeger and Kleiner. Summary written for 2009 Summer School on Geometry and analysis in the theory of computation at Indiana University. pdf

Teaching

• January-March 2012
  • Gromov hyperbolic groups and their boundaries, Taught Course Centre. Course information
• Old teaching information.

Links

At the University of Oxford, I am primarily working with Cornelia Drutu 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 Edinburgh.