Sam Shepherd

Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville, TN 37240

I am currently a postdoc at Vanderbilt University. I completed my PhD at the University of Oxford, under the supervision of Martin Bridson.
Here is my CV.

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.


Separability properties of higher-rank GBS groups , with Jone Lopez de Gamiz Zearra, arXiv, 2023

Splittings of one-ended groups with one-ended halfspaces and non-1-acyclicity at infinity, with Michael Mihalik, arXiv, 2023

Graphically discrete groups and rigidity, with Alex Margolis, Emily Stark and Daniel J. Woodhouse, arXiv, 2023 

Published or accepted for publication

Semistability of cubulated groups, Math. Ann. 387, no. 3-4, 2023 

Imitator homomorphisms for special cube complexes, Trans. Amer. Math. Soc. 376, no. 1, 2023 

Commensurability of lattices in right-angled buildings, arXiv, 2022, to appear in Adv. Math.

A cubulation with no factor system, arXiv, 2022, to appear in Algebr. Geom. Topol.

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, with Martin R. Bridson,  Algebr. Geom. Topol. 22 (2), 2022

Quasi-isometric rigidity for graphs of virtually free groups with two-ended edge groups, with Daniel J. Woodhouse,  J. Reine Angew. Math. 782, 2022

Agol's theorem on hyperbolic cubulations, Rocky Mountain J. Math. 51 (3),  2021