Dr Anne Thomas

F07 - Carslaw Building
The University of Sydney

Research interests

I am a member of the Geometry, Topology and Analysis Research Group.

My research interests include geometric group theory and rigidity. I use a variety of methods from analysis, combinatorics, group theory and topology to investigate polyhedral complexes, including buildings, lattices in automorphism groups of such complexes, and related topics such as Coxeter groups. Many questions are motivated by the study of lattices in semisimple Lie groups. For an overview, see my survey paper with Benson Farb and Chris Hruska, which presents many open research problems.

Current research students

Project title Research student
Geometric Structures on 3-Manifolds Dickson Yaw Badu Annor ANNOR
Scale multiplicative semigroups of groups acting on trees with almost prescribed local action Tim BYWATERS
Decompositions of Moduli Spaces of Real Projective Structures Dominic TATE

Selected grants

2011

  • Lattices in locally compact groups; Thomas A, Capdeboscq I; Australian Research Council (ARC)/Discovery Projects (DP).

Selected publications

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Book Chapters

  • Thomas, A. (2016). Lattices in hyperbolic buildings. In C S Aravinda, F T Farrell, J-F Lafont (Eds.), Geometry, Topology, and Dynamics in Negative Curvature, (pp. 345-363). UK: Cambridge University Press.
  • Farb, B., Hruska, C., Thomas, A. (2011). Problems on automorphism groups of nonpositively curved polyhedral complexes and their lattices. In Benson Farb and David Fisher (Eds.), Geometry, Rigidity, and Group Actions, (pp. 515-560). USA: The University of Chicago Press.

Journals

  • Giudici, M., Li, C., Seress, A., Thomas, A. (2015). Characterising vertex-star transitive and edge-star transitive graphs. Israel Journal of Mathematics, 205(1), 35-72. [More Information]
  • Capdeboscq, I., Rumynin, D., Thomas, A. (2015). Cocompact lattices on \tilde{A}_n buildings buildings. Glasgow Mathematical Journal, 57, 241-256. [More Information]
  • Dani, P., Thomas, A. (2015). Divergence in right-angled Coxeter groups. Transactions of the American Mathematical Society, 367(5), 3549-3577. [More Information]
  • Lam, T., Thomas, A. (2015). Infinite Reduced Words and the Tits Boundary of a Coxeter Group. International Mathematics Research Notices, 2015 (17), 7690-7733. [More Information]
  • Capdeboscq, I., Thomas, A. (2013). Co-compact lattices in complete Kac-Moody groups with Weyl group right-angled or a free product of spherical special subgroups. Mathematical Research Letters, 20(2), 339-358.
  • Capdeboscq, I., Thomas, A. (2013). Cocompact lattices in complete kac-moody groups with weyl group right-angled or a free product of spherical special subgroups. Mathematical Research Letters, 20(2), 339-358. [More Information]
  • Kubena, A., Thomas, A. (2012). Density of commensurators for uniform lattices of right-angled buildings. Journal of Group Theory, 15(5), 565-611. [More Information]
  • Thomas, A. (2012). Existence, covolumes and infinite generation of lattices for Davis complexes. Groups, Geometry and Dynamics, 6(4), 765-801. [More Information]
  • Capdeboscq, I., Thomas, A. (2012). Lattices in complete rank 2 Kac-Moody groups. Journal of Pure and Applied Algebra, 216(2012), 1348-1371. [More Information]
  • Futer, D., Thomas, A. (2012). Surface quotients of hyperbolic buildings. International Mathematics Research Notices, 2012 (2), 437-477. [More Information]
  • Thomas, A., Wortman, K. (2011). Infinite generation of non-cocompact lattices on right-angled buildings. Algebraic and Geometric Topology, 11(2), 929-938. [More Information]
  • Lim, S., Thomas, A. (2010). Counting Overlattices for Polyhedral Complexes. Topology Proceedings, 36, 229-247.
  • Lim, S., Thomas, A. (2008). Covering Theory for Complexes of Groups. Journal of Pure and Applied Algebra, 212(7), 1632-1663. [More Information]
  • Thomas, A. (2007). Covolumes of Uniform Lattices Acting on Polyhedral Complexes. Bulletin of the London Mathematical Society, 39, 103-111. [More Information]
  • Thomas, A. (2007). On the set of covolumes of lattices for Fuchsian buildings. Academie des Sciences. Comptes Rendus. Mathematique, 344, 215-218. [More Information]
  • Thomas, A. (2006). Lattices acting on right-angled buildings. Algebraic and Geometric Topology, 6, 1215-1238. [More Information]

2016

  • Thomas, A. (2016). Lattices in hyperbolic buildings. In C S Aravinda, F T Farrell, J-F Lafont (Eds.), Geometry, Topology, and Dynamics in Negative Curvature, (pp. 345-363). UK: Cambridge University Press.

2015

  • Giudici, M., Li, C., Seress, A., Thomas, A. (2015). Characterising vertex-star transitive and edge-star transitive graphs. Israel Journal of Mathematics, 205(1), 35-72. [More Information]
  • Capdeboscq, I., Rumynin, D., Thomas, A. (2015). Cocompact lattices on \tilde{A}_n buildings buildings. Glasgow Mathematical Journal, 57, 241-256. [More Information]
  • Dani, P., Thomas, A. (2015). Divergence in right-angled Coxeter groups. Transactions of the American Mathematical Society, 367(5), 3549-3577. [More Information]
  • Lam, T., Thomas, A. (2015). Infinite Reduced Words and the Tits Boundary of a Coxeter Group. International Mathematics Research Notices, 2015 (17), 7690-7733. [More Information]

2013

  • Capdeboscq, I., Thomas, A. (2013). Co-compact lattices in complete Kac-Moody groups with Weyl group right-angled or a free product of spherical special subgroups. Mathematical Research Letters, 20(2), 339-358.
  • Capdeboscq, I., Thomas, A. (2013). Cocompact lattices in complete kac-moody groups with weyl group right-angled or a free product of spherical special subgroups. Mathematical Research Letters, 20(2), 339-358. [More Information]

2012

  • Kubena, A., Thomas, A. (2012). Density of commensurators for uniform lattices of right-angled buildings. Journal of Group Theory, 15(5), 565-611. [More Information]
  • Thomas, A. (2012). Existence, covolumes and infinite generation of lattices for Davis complexes. Groups, Geometry and Dynamics, 6(4), 765-801. [More Information]
  • Capdeboscq, I., Thomas, A. (2012). Lattices in complete rank 2 Kac-Moody groups. Journal of Pure and Applied Algebra, 216(2012), 1348-1371. [More Information]
  • Futer, D., Thomas, A. (2012). Surface quotients of hyperbolic buildings. International Mathematics Research Notices, 2012 (2), 437-477. [More Information]

2011

  • Thomas, A., Wortman, K. (2011). Infinite generation of non-cocompact lattices on right-angled buildings. Algebraic and Geometric Topology, 11(2), 929-938. [More Information]
  • Farb, B., Hruska, C., Thomas, A. (2011). Problems on automorphism groups of nonpositively curved polyhedral complexes and their lattices. In Benson Farb and David Fisher (Eds.), Geometry, Rigidity, and Group Actions, (pp. 515-560). USA: The University of Chicago Press.

2010

  • Lim, S., Thomas, A. (2010). Counting Overlattices for Polyhedral Complexes. Topology Proceedings, 36, 229-247.

2008

  • Lim, S., Thomas, A. (2008). Covering Theory for Complexes of Groups. Journal of Pure and Applied Algebra, 212(7), 1632-1663. [More Information]

2007

  • Thomas, A. (2007). Covolumes of Uniform Lattices Acting on Polyhedral Complexes. Bulletin of the London Mathematical Society, 39, 103-111. [More Information]
  • Thomas, A. (2007). On the set of covolumes of lattices for Fuchsian buildings. Academie des Sciences. Comptes Rendus. Mathematique, 344, 215-218. [More Information]

2006

  • Thomas, A. (2006). Lattices acting on right-angled buildings. Algebraic and Geometric Topology, 6, 1215-1238. [More Information]

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