David Hume

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About me

I am currently a Titchmarsh Research Fellow in the Topology group at the University of Oxford, a Junior Research Fellow at St Cross College and an Enterprise Fellow of the Mathematical, Physical and Life Sciences Division. Previously, I spent two years at UCLouvain working with Pierre-Emmanuel Caprace, a year at Université Paris-Sud, Orsay working with Romain Tessera, and was the (first) McDuff Postdoctoral Fellow at the Mathematical Sciences Research Institute for the Fall 2016 semester.

I completed my PhD at the University of Oxford under the supervision of Cornelia Drutu, and wrote a Master's thesis at the University of Birmingham under the supervision of Ralf Köhl.

Research interests

Geometric group theory
Gromov hyperbolic groups and their generalisations
Coarse geometry and embeddings

Teaching

In spring 2018 I taught a graduate (TCC) course on Totally Disconnected Locally Compact Groups.

Outreach

Some of my ramblings about expanders can be found here.

Published Papers

Poincaré profiles of groups and spaces, joint with John Mackay and Romain Tessera. To appear in Revista Matematica Iberoamericana. Preprint.
Extending group actions on metric spaces, joint with Carolyn Abbott and Denis Osin. To appear in the Journal of Topology and Analysis. Preprint.
Relatively hyperbolic groups with fixed peripherals, joint with Matthew Cordes. Israel Journal of Mathematics 230(1):443–470, 2019. Preprint.
Contracting geodesics in infinitely presented graphical small cancellation groups, joint with Goulnara Arzhantseva, Christopher H. Cashen, and Dominik Gruber. Groups, Geometry and Dynamics 13:579–632, 2018. Preprint
Groups with no coarse embeddings into hyperbolic groups, joint with Alessandro Sisto. New York Journal of Mathematics 23:1657–1670, 2017. Preprint.
Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction, joint with Goulnara Arzhantseva, Christopher H. Cashen, and Dominik Gruber, Documenta Mathematica 22:193–1224, 2017. Preprint.
Stability and the Morse boundary, joint with Matthew Cordes, Journal of the London Mathematical Society 95(2), no. 3, 963–988, 2017. Preprint.
Embedding mapping class groups into finite products of trees, Groups, Geometry and Dynamics 11(2):613-647, 2017. Preprint.
A continuum of expanders, Fundamenta Mathematicae 237: 143-152, 2017. Preprint.
Orthogonal Forms of Kac-Moody groups are acylindrically hyerpbolic, joint with Pierre-Emmanuel Caprace. Annales de l'Institut Fourier 65(6):2613–2640, 2015. Preprint.
Direct Embeddings of Relatively Hyperbolic Groups with Optimal \ell^p Compression Exponent. Journal für die Reine und Angewandte Mathematik 703: 147-172, 2015. Preprint.
Embedding Universal Covers of Graph Manifolds in Products of Trees, joint with Alessandro Sisto Proceedings of the American Mathematical Society 141:3337-3340, 2013. Preprint.

Book Chapters

The Centraliser Lattice, joint with Thierry Stulemeijer. In “New Directions in Locally Compact Groups” edited by Pierre-Emmanuel Caprace and Nicolas Monod. LMS Lecture Note Series 447, Cambridge University Press, 2018.

Selected Preprints

Poorly Connected Groups, joint with John Mackay. Preprint.
Actions of small cancellation groups on hyperbolic spaces, joint with Carolyn Abbott. Preprint.
The geometry of generalised loxodromic elements, joint with Carolyn Abbott. Preprint.

My theses

Embeddings of infinite groups into Banach spaces, DPhil thesis, University of Oxford, 2013.
Extensions of Borovoi's theorem, Master's thesis, University of Birmingham, 2009.

Upcoming conference talks

https://sites.google.com/view/gagta2020 Edinburgh, June 2020.
Of coarse! Quasi-isometries: rigidity and classification Ventotene, Italy, Sep 2019.
Groups with hyperbolic features ETH Zurich, Aug 2019.

Previous conference talks

Young Geometric Group Theory VII, Les Diablerets, Switzerland 2018 (Invited)
Asymptotic decomposition methods in geometry, dynamics and operator algebras, University of Southampton, April 2017
Non-positive curvature in action, INI Cambridge, January 2017
Generalizations of Symmetric Spaces, Nahsholim, Israel, June 2015
Arbeitsgemeinschaft: Totally Disconnected Groups, MRI Oberwolfach, October 2014
Geometry on Groups and Spaces (ICM Satellite), KAIST, Daejeon, South Korea, August 2014
American Mathematical Society Western Sectional Meeting, University of Hawaii at Manoa, February 2012

Contact information

E-mail: david [dot] hume [at] maths [dot] ox [dot] ac [dot] uk