Research
I am a member of the Geometry, Topology and Analysis Group.
My research interests include geometric group theory, Coxeter groups and buildings. Most of my work concerns actions of discrete groups on nonpositively curved spaces, and I often collaborate with researchers from other areas of mathematics.
My papers on the arXiv are available here.
Publications and preprints
- A gallery model for affine flag varieties via chimney retractions.
with Elizabeth Milićević, Yusra Naqvi and Petra Schwer
submitted. (pdf)
- Geometric and topological aspects of Coxeter groups and buildings
Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zurich, 2018.(published version)
- Automorphism groups of combinatorial structures
2016 MATRIX annals, 561–592, MATRIX Book Ser., 1, Springer, Cham, 2018.(published version)
- Commensurability for certain right-angled Coxeter groups and geometric amalgams of free groups.
with Pallavi Dani and Emily Stark
Groups Geom. Dyn. 12 (2018), 1273-1341. (published version)(pdf)
- Maximal torsion-free subgroups of certain lattices of hyperbolic buildings and Davis complexes.
with William Norledge and Alina Vdovina
Geom. Dedicata 192 (2018), 121-143. (published version)(pdf)
- C*-algebras associated to graphs of groups.
with Nathan Brownlowe, Alexander Mundey, David Pask and Jack Spielberg
Adv. Math. 316 (2017), 114-186. (published version)(pdf)
- Bowditch's JSJ tree and the quasi-isometry classification of certain Coxeter groups.
with Pallavi Dani
J. Topol. 10 (2017), 1066-1106. (published version)(pdf)
- Palindromic automorphisms of right-angled Artin groups.
with Neil J. Fullarton
Groups Geom. Dyn. 12 (2018), 865-887. (published version)(pdf)
- Dimensions of affine Deligne-Lusztig varieties: a new approach via labeled folded alcove walks and root operators.
with Elizabeth Milićević and Petra Schwer
Mem. Amer. Math. Soc. 261 (2019), no. 1260. (published version)(pdf)
- Characterising vertex-star transitive and edge-star transitive graphs.
with Michael Giudici, Cai-Heng Li and Ákos Seress
Israel J. Math. 205 (2015), 35-72. (published version)(pdf)
- Infinite reduced words and the Tits boundary of a Coxeter group.
with Thomas Lam
Int. Math. Res. Not. (2015) Vol. 2015 7690-7733. (published version)(pdf)
- Divergence in right-angled Coxeter groups.
with Pallavi Dani
Trans. Amer. Math. Soc. 367 (2015), 3549-3577. (published version)(pdf)
- Quasi-isometries
with Dan Margalit, in "Office Hours with a Geometric Group Theorist", Princeton University Press, 2017. (published version)
- Cocompact lattices in complete Kac-Moody groups with Weyl group right-angled or a free product of spherical special subgroups.
with Inna Capdeboscq
Math. Res. Lett. 20 (2013) 339-358. (published version)(pdf)
- Cocompact lattices on Ãn buildings.
with Inna Capdeboscq and Dmitriy Rumynin
Glasgow Math. J. 57 (2015), 241-262. (published version)(pdf)
- Lattices in hyperbolic buildings.
In "Geometry, Topology, and Dynamics in Negative Curvature", C. S. Aravinda, F. T. Farrell and J.-F. Lafont (eds), London Mathematical Society Lecture Note Series, Vol. 425, Cambridge University Press, Cambridge, 2016. (pdf)
- Infinite generation of non-cocompact lattices on right-angled buildings.
with Kevin Wortman
Algebr. Geom. Top. 11 (2011) 929-938. (published version)(pdf)
- Surface quotients of hyperbolic buildings.
with David Futer
Int. Math. Res. Notices (2012) Vol. 2012 437-477. (published version)
- Lattices in complete rank 2 Kac-Moody groups.
with Inna (Korchagina) Capdeboscq
J. Pure Appl. Algebra 216 (2012), 1348-1371. (published version)(pdf)
- Density of commensurators for uniform lattices of right-angled
buildings.
with Angela Kubena
J. Group Theory 15 (2012), 565-611. (published version)(pdf)
- Existence, covolumes and infinite generation of lattices for Davis
complexes.
Groups Geom. Dyn. 6 (2012), 765-801. (published version)(pdf)
- Problems on automorphism groups of nonpositively curved polyhedral
complexes and their lattices.
with Benson Farb and G. Christopher Hruska
In "Geometry, Rigidity, and Group Actions", Benson Farb and David Fisher (eds), The University of Chicago Press, Chicago 2011. (published version)
- On the set of covolumes of lattices for Fuchsian buildings.
C. R. Acad. Sci. Paris, Ser. I 344 (2007) 215-218. (published version)(pdf)
- Counting overlattices for polyhedral complexes.
with Seonhee Lim
Top. Proc. 36 (2010) 229-247. (published version)(pdf)
- Covering theory for complexes of groups.
with Seonhee Lim
J. Pure Appl. Algebra 212 (2008) 1632-1663. (published version)(pdf)
- Lattices acting on right-angled buildings.
Algebr. Geom. Topol. 6 (2006) 1215-1238. (published version)(pdf)
- Covolumes of uniform lattices acting on polyhedral complexes.
Bull. London Math. Soc. 39 (2007) 103-111. (published version)(pdf)