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John Mackay

Associate Professor (Reader)

School of Mathematics,
Fry Building, Woodland Road, Bristol, BS8 1UG, UK.

Research

I 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. 36 (2020), no. 6, 1835-1886. arxiv:1707.02151 pdf journal version
• Poorly connected groups, with D. Hume, Proc. Amer. Math. Soc. 148 (2020), 4653-4664. arxiv:1904.04639 pdf journal version
• Random triangular Burnside groups, with D. Gruber, Israel J. Math. 244, 75-94 (2021). arxiv:1810.01805 pdf journal version
• Conformal dimension of hyperbolic groups that split over elementary subgroups, with M. Carrasco, Invent. Math. 227 (2022), no. 2, 795-854. arxiv:2007.09030 pdf journal version
• Poincaré profiles of Lie groups and a coarse geometric dichotomy, with D. Hume and R. Tessera, Geom. Func. Anal. 32, 1063-1133 (2022). arxiv:2011.02963 pdf journal version
• Maps between relatively hyperbolic spaces and between their boundaries, with A. Sisto, Trans. Amer. Math. Soc. 377 (2024), 1409-1454. arxiv:2012.11902 pdf journal version

Preprints

• Asymptotic dimension for covers with controlled growth, with D. Hume and R. Tessera, preprint. arxiv:2303.01969 pdf
• Actions of acylindrically hyperbolic groups on ℓ¹, with C. Drutu, preprint. arxiv:2309.12915 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-May 2024 (Teaching block 2)
  • Introduction to Group Theory (part of Introduction to Proofs and Group Theory). Course information on Blackboard.
• Old teaching information.

Conferences

• Geometry and analysis of groups and manifolds, Pisa, June 2023
• New Perspectives in Pure Mathematics, Bristol, March 2023
• CMI-HIMR Dynamics and Geometry (Online) Summer School, Bristol, June 2021
• Probability, Analysis and Dynamics conference, Bristol, April 20212022
• Interactions between Geometry, Dynamics and Group Theory, LMS South West and South Wales regional meeting and workshop, Bristol, January 2020
• Probability, Analysis and Dynamics conference, Bristol, April 2018
• BMC Analysis workshop, Bristol, March 2016
• MSRI Summer Graduate School on Geometric Group Theory, MSRI, June 2015

Links

At 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.