Samuel Shepherd
Postdoctoral Scholar
Research Interests
Geometric Group Theory and Topology; including CAT(0) cube complexes and specialness, Leighton’s graph covering theorem and generalisations, and quasi-isometric rigidity.
Publications
- Graphically discrete groups and rigidity (joint with Alex Margolis, Emily Stark and Daniel J. Woodhouse), arXiv:2303.04843, 2023
- Imitator homomorphisms for special cube complexes, Trans. Amer. Math. Soc. 376, no. 1, 2023
- A cubulation with no factor system, arXiv:2208.10421, 2022, to appear in Algebr. Geom. Topol.
- Commensurability of lattices in right-angled buildings, arXiv:2203.01210, 2022, to appear in Adv. Math.
- Two generalisations of Leighton's theorem (with an appendix by Giles Gardam and Daniel J. Woodhouse), Groups Geom. Dyn. 16, no. 3, 2022
- Leighton's Theorem: extensions, limitations, and quasitrees (joint with Martin R. Bridson), Algebr. Geom. Topol. 22 (2), 2022
- Quasi-isometric rigidity for graphs of virtually free groups with two-ended edge groups (joint with Daniel J. Woodhouse), J. Reine Angew. Math. 782, 2022
- Agol's theorem on hyperbolic cubulations, Rocky Mountain J. Math. 51 (3), 2021