Research

My research interests include geometric group theory and rigidity. I use methods of geometric group theory to study lattices in automorphism groups of polyhedral complexes, including buildings. Many questions are motivated by the study of lattices in Lie groups. For more details, see my research statement.

Papers

• Cocompact lattices of minimal covolume in rank 2 Kac-Moody groups, Part I: Edge-transitive lattices (pdf)
  (with Inna (Korchagina) Capdeboscq ), submitted.
  
  
• Density of commensurators for uniform lattices of right-angled buildings (pdf)
  (with Angela Kubena Barnhill), submitted.
  
  
• Existence, covolumes and infinite generation of lattices for Davis complexes (pdf)
  submitted.
  
  
• Problems on automorphism groups of nonpositively curved polyhedral complexes and their lattices (pdf)
  (with Benson Farb and G. Christopher Hruska), to appear in Festschrift for Robert Zimmer's 60th birthday.
  
  
• Lattices in trees and higher-dimensional complexes (pdf)
  (with Benson Farb and Shahar Mozes), in wiki Problems in Geometric Group Theory.
  
  
• On the set of covolumes of lattices for Fuchsian buildings (pdf)
  C. R. Acad. Sci. Paris, Ser. I 344 (2007) 215-218.
  
  
• Counting overlattices for polyhedral complexes (pdf)
  (with Seonhee Lim), submitted.
  
  
• Covering theory for complexes of groups (pdf)
  (with Seonhee Lim) J. Pure Appl. Algebra 212 (2008) 1632-1663.
  
  
• Lattices acting on right-angled buildings (pdf)
  Algebr. Geom. Topol. 6 (2006) 1215-1238.
  
  
• Covolumes of uniform lattices acting on polyhedral complexes (pdf)
  Bull. London Math. Soc. 39 (2007) 103-111.