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## John Mackay## LecturerSchool of Mathematics,
## ResearchI am interested in many things geometric; in particular, analysis on metric spaces, geometric group theory, hyperbolic groups ... ## Papers*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. Errata.*Assouad dimension of self-affine carpets*, Conform. Geom. Dyn. 15 (2011), 177-187.`arxiv:1003.0930`pdf journal version.*Conformal dimension and random groups*, Geom. Funct. Anal. Volume 22, Number 1 (2012), 213-239.`arxiv:1011.3167`pdf journal version*Modulus and Poincaré inequalities on non-self-similar Sierpinski carpets*, with J. T. Tyson and K. Wildrick, Geom. Funct. Anal. Volume 23, Number 3 (2013), 985-1034.`arxiv:1201.3548`pdf journal version*Embedding relatively hyperbolic groups in products of trees*, with A. Sisto, Alg. Geom. Top., Volume 13 (2013) 2261-2282.`arxiv:1207.3008`pdf journal version*Quasi-circles through prescribed points*, Indiana U. Math. J., Volume 63 No. 2 (2014), 403-417.`arxiv:1210.5119`pdf journal version*Balanced walls for random groups*, with P. Przytycki, Michigan Math. J., Volume 64, Issue 2 (2015), 397-419.`arxiv:1407.0332`pdf journal version*Differentiable structures on metric measure spaces: A Primer*, with B. Kleiner, Annali SNS, Volume XVI, Issue 1 (2016), 41-64.`arxiv:1108.1324`pdf journal version*Conformal dimension via subcomplexes for small cancellation and random groups*, Math. Ann. 364 (2016), no. 3-4, 937-982.`arxiv:1409.0802`pdf journal version*A sharper threshold for random groups at density one-half*, with M. Duchin, K. Jankiewicz, S. C. Kilmer, S. Lelièvre, A. P. Sánchez, Groups Geom. Dyn., Volume 10, Issue 3, 2016, pp. 985-1005.`arxiv:1412.8741`pdf journal version*Random groups, random graphs and eigenvalues of p-Laplacians*, with C. Drutu, Adv. Math., Volume 341, 2019, pp. 188-254.`arxiv:1607.04130`pdf journal version*A metrizable topology on the contracting boundary of a group*, with C. Cashen, Trans. Amer. Math. Soc. 372 (2019), no. 3, 1555-1600.`arxiv:1703.01482`pdf journal version*Quasi-hyperbolic planes in relatively hyperbolic groups*, with A. Sisto, Ann. Acad. Sci. Fenn. Math., Volume 45, 2020, 139-174.`arxiv:1111.2499`pdf journal version*Poincaré profiles of groups and spaces*, with D. Hume and R. Tessera, Rev. Mat. Iberoam., to appear.`arxiv:1707.02151`pdf journal version*Poorly connected groups*, with D. Hume, Proc. Amer. Math. Soc., to appear.`arxiv:1904.04639`pdf*Random triangular Burnside groups*, with D. Gruber, Israel J. Math., to appear.`arxiv:1810.01805`pdf
## Preprints*Conformal dimension of hyperbolic groups that split over elementary subgroups*, with M. Carrasco, preprint.`arxiv:2007.09030`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 L*, after Cheeger and Kleiner. Summary written for 2009 Summer School on Geometry and analysis in the theory of computation at Indiana University. pdf^{1}
## Teaching- January-May 2021 (Teaching block 2)
- Introduction to Geometry. Course information on Blackboard.
- Old teaching information.
## Conferences- Probability, Analysis and Dynamics conference, April 2021
- Interactions between Geometry, Dynamics and Group Theory, LMS South West and South Wales regional meeting and workshop, January 2020
- Probability, Analysis and Dynamics conference, April 2018
- BMC Analysis workshop, March 2016
- MSRI Summer Graduate School on Geometric Group Theory, June 2015
## LinksAt the University of Bristol, I am a member of the Probability, Analysis and Dynamics and the Pure Mathematics institutes. Previously, from 2011-2013 I was a postdoc at the University of Oxford working with Cornelia Drutu and other members in the topology group. Before that, 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. |