Dr David Hume MSci DPhil

Dr David Hume

School of Mathematics
Assistant Professor

Contact details

Email
d.hume@bham.ac.uk
View my research portal
Address
School of Mathematics
Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

David is a geometric group theorist, specialising in coarse geometry and its interactions with several other branches of mathematics and computer science. He is a member of the Algebra group in the School of Mathematics.

David currently holds an EPSRC Fellowship EP/V027360/1, Coarse Geometry of Groups and Spaces.

Departmental webpage.

Qualifications

  • DPhil in Mathematics, University of Oxford, 2013
  • MSci in Mathematical Sciences, University of Birmingham, 2009

Biography

David completed his MSci in Mathematical Sciences at the University of Birmingham in 2009. He went on to study for a DPhil in Geometric Group Theory at the University of Oxford under the supervision of Cornelia Druțu. Since then, he has held PDRA positions in Bar-Ilan University, Tel-Aviv; UCLouvain, Belgium; and Université Paris XI Orsay, France; and Research Fellowships at MSRI (now SLMath), and the Universities of Oxford and Bristol.

Postgraduate supervision

I am interested in all aspects of geometric group theory and related topics. My current PhD student is working on relatively hyperbolic groups. Previous 3rd and 4th year project students have worked on topics including expander graphs, the growth function, asymptotic dimension and random groups. UG Summer Research students have worked on fractal geometry, network wiring problems, and various graph theoretic invariants such as treewidth and cutwidth.

Research

Research themes

  • Geometric Group Theory
  • Coarse Geometry of Groups and Spaces
  • Hyperbolic Groups and their Generalisations
  • Expander Graphs and Complexes

Research activity

David's recent research concerns properties of metric spaces which are robust under a large and natural class of functions called regular maps: examples include certain measures of robust connectivity and notions of large-scale dimension. He regularly collaborates with John Mackay (University of Bristol) and Romain Tessera (Jussieu-Paris Rive Gauche).

Publications

Recent publications

Article

Hume, D, Mackay, JM & Tessera, R 2022, 'Poincaré profiles of Lie groups and a coarse geometric dichotomy', Geometric and Functional Analysis, vol. 32, no. 5, pp. 1063–1133. https://doi.org/10.1007/s00039-022-00617-4

Abbott, C & Hume, D 2021, 'Actions of small cancellation groups on hyperbolic spaces', Geometriae Dedicata, vol. 212, no. 1, pp. 325–363. https://doi.org/10.1007/s10711-020-00561-3

Abbott, CR & Hume, D 2021, 'The geometry of generalized loxodromic elements', Annales de l'Institut Fourier, vol. 70, no. 4, pp. 1689-1713. https://doi.org/10.5802/aif.3379

Abbott, C, Hume, D & Osin, D 2020, 'Extending group actions on metric spaces', Journal of Topology and Analysis. https://doi.org/10.1142/s1793525319500584

Hume, D, Mackay, J & Tessera, R 2020, 'Poincaré profiles of groups and spaces', Revista Matematica Iberoamericana . https://doi.org/10.4171/rmi/1184

Hume, D & Mackay, JM 2020, 'Poorly connected groups', Proceedings of the American Mathematical Society. https://doi.org/10.1090/proc/15128

Arzhantseva, G, Cashen, C, Gruber, D & Hume, D 2019, 'Negative curvature in graphical small cancellation groups', Groups, Geometry, and Dynamics. https://doi.org/10.4171/ggd/498

Cordes, M & Hume, D 2019, 'Relatively hyperbolic groups with fixed peripherals', Israel Journal of Mathematics. https://doi.org/10.1007/s11856-019-1830-5

Hume, D 2017, 'A continuum of expanders', Fundamenta Mathematicae. https://doi.org/10.4064/fm101-11-2016

Arzhantseva, GN, Cashen, CH, Gruber, D & Hume, D 2017, 'Characterizations of Morse Quasi-Geodesics via Superlinear Divergence and Sublinear Contraction', Documenta Mathematica. https://doi.org/10.4171/dm/592

Hume, D 2017, 'Embedding mapping class groups into a finite product of trees', Groups, Geometry, and Dynamics. https://doi.org/10.4171/ggd/410

Hume, D & Sisto, A 2017, 'Groups with no coarse embeddings into hyperbolic groups', New York Journal of Mathematics.

Chapter

Hume, D & Stulemeijer, T 2018, The centraliser lattice. in New Directions in Locally Compact Groups. https://doi.org/10.1017/9781108332675.019

Preprint

Hume, D, Mackay, JM & Tessera, R 2023 'Asymptotic dimension for covers with controlled growth' arXiv, pp. 1-39. https://doi.org/10.48550/arXiv.2303.01969

Barrett, B & Hume, D 2021 'Thick embeddings of graphs into symmetric spaces via coarse geometry' arXiv, pp. 1-27. https://doi.org/10.48550/arXiv.2112.05305

View all publications in research portal