Dr Stephan Tillmann

F07 - Carslaw Building
The University of Sydney

Telephone 9351 2005
Fax 9351 4534

Website Personal web page

Research interests

Stephan Tillmann is a member of the Geometry, Topology and Analysis Research Group. Stephan's main research interests are geometry and topology with a focus on low-dimensional manifolds. He uses techniques from algebraic geometry, hyperbolic and projective geometry, geometric group theory, representations of finitely generated groups, differential geometry as well as tropical geometry. A principal aim of his current research is to understand the relationship between triangulations of, geometric structures on, and surfaces in 3-manifolds with view towards new topological results about 3-manifolds, practical algorithms, and applications to group theory.

Teaching and supervision

Timetable

Selected grants

2014

  • Moduli spaces of geometric structures; Tillmann S; Australian Research Council (ARC)/Discovery Projects (DP).

2013

  • Triangulations in dimensions 3 and 4: discrete and geometric structures; Rubinstein H, Hodgson C, Tillmann S; Australian Research Council (ARC)/Discovery Projects (DP).

2011

  • Generic complexity in computational topology: breaking through the bottlenecks; Burton B, Elder M, Tillmann S; Australian Research Council (ARC)/Discovery Projects (DP).

2010

  • Triangulations in dimension three: algorithms and geometric structures; Tillmann S, Rubinstein H, Hodgson C; Australian Research Council (ARC)/Discovery Projects (DP).

Selected publications

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Journals

  • Luo, F., Tillmann, S., Yang, T. (2013). Thurston's spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3-manifolds. Proceedings of the American Mathematical Society, 141(1), 335-350. [More Information]
  • Tillmann, S. (2012). Degenerations of ideal hyperbolic triangulations. Mathematische Zeitschrift, 272(3-4), 793-823. [More Information]
  • Burton, B., Rubinstein, H., Tillmann, S. (2012). The Weber-Seifert dodecahedral space is non-haken. Transactions of the American Mathematical Society, 364(2), 911-932. [More Information]
  • Jaco, W., Rubinstein, H., Tillmann, S. (2011). Coverings and minimal triangulations of 3–manifolds. Algebraic and Geometric Topology, 11(3), 1257-1265. [More Information]
  • Tillmann, S. (2011). Geometry and Topology Down Under. Gazette of the Australian Mathematical Society, 38(5), 261-263.
  • Hodgson, C., Rubinstein, H., Segerman, H., Tillmann, S. (2011). Veering triangulations admit strict angle structures. Geometry and Topology, 15(4), 2073-2089. [More Information]
  • Jaco, W., Rubinstein, H., Tillmann, S. (2009). Minimal triangulations for an infinite family of lens spaces. Journal of Topology, 2(1), 157-180. [More Information]
  • Cooper, D., Tillmann, S. (2009). The Thurston norm via normal surfaces. Pacific Journal of Mathematics, 239(1), 1-15. [More Information]
  • Luo, F., Tillmann, S. (2008). Angle structures and normal surfaces. Transactions of the American Mathematical Society, 360(6), 2849-2866. [More Information]
  • Luo, F., Schleimer, S., Tillmann, S. (2008). Geodesic ideal triangulations exist virtually. Proceedings of the American Mathematical Society, 136(7), 2625-2630. [More Information]
  • Tillmann, S. (2008). Normal surfaces in topologically finite 3-manifolds. L'Enseignement Mathematique, 54(2), 329-380.
  • Chesebro, E., Tillmann, S. (2007). Not all boundary slopes are strongly detected by the character variety. Communications in Analysis and Geometry, 15(4), 695-723.
  • Tillmann, S. (2005). Boundary slopes and the logarithmic limit set. Topology, 44(1), 203-216.
  • Tillmann, S. (2004). Character varieties of mutative 3–manifolds. Algebraic and Geometric Topology, 4, 133-149.
  • Tillmann, S. (2000). On the Kinoshita-Terasaka knot and generalised Conway mutation. Journal of Knot Theory and Its Ramifications, 9(4), 557-575. [More Information]

Conferences

  • Burton, B., Coward, A., Tillmann, S. (2013). Computing Closed Essential Surfaces in Knot Complements. SoCG 13 The twenty-ninth annual symposium on Computational geometry 2013, New York: ACM Digital Library. [More Information]
  • Tillmann, S. (2012). Structure of 0–efficient or minimal triangulations. Triangulations Workshop, Zurich: EMS Publishing House.
  • Segerman, H., Tillmann, S. (2011). Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations. Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures, Stillwater, OK, USA: Oklahoma State University. [More Information]

2013

  • Burton, B., Coward, A., Tillmann, S. (2013). Computing Closed Essential Surfaces in Knot Complements. SoCG 13 The twenty-ninth annual symposium on Computational geometry 2013, New York: ACM Digital Library. [More Information]
  • Luo, F., Tillmann, S., Yang, T. (2013). Thurston's spinning construction and solutions to the hyperbolic gluing equations for closed hyperbolic 3-manifolds. Proceedings of the American Mathematical Society, 141(1), 335-350. [More Information]

2012

  • Tillmann, S. (2012). Degenerations of ideal hyperbolic triangulations. Mathematische Zeitschrift, 272(3-4), 793-823. [More Information]
  • Tillmann, S. (2012). Structure of 0–efficient or minimal triangulations. Triangulations Workshop, Zurich: EMS Publishing House.
  • Burton, B., Rubinstein, H., Tillmann, S. (2012). The Weber-Seifert dodecahedral space is non-haken. Transactions of the American Mathematical Society, 364(2), 911-932. [More Information]

2011

  • Jaco, W., Rubinstein, H., Tillmann, S. (2011). Coverings and minimal triangulations of 3–manifolds. Algebraic and Geometric Topology, 11(3), 1257-1265. [More Information]
  • Tillmann, S. (2011). Geometry and Topology Down Under. Gazette of the Australian Mathematical Society, 38(5), 261-263.
  • Segerman, H., Tillmann, S. (2011). Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations. Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures, Stillwater, OK, USA: Oklahoma State University. [More Information]
  • Hodgson, C., Rubinstein, H., Segerman, H., Tillmann, S. (2011). Veering triangulations admit strict angle structures. Geometry and Topology, 15(4), 2073-2089. [More Information]

2009

  • Jaco, W., Rubinstein, H., Tillmann, S. (2009). Minimal triangulations for an infinite family of lens spaces. Journal of Topology, 2(1), 157-180. [More Information]
  • Cooper, D., Tillmann, S. (2009). The Thurston norm via normal surfaces. Pacific Journal of Mathematics, 239(1), 1-15. [More Information]

2008

  • Luo, F., Tillmann, S. (2008). Angle structures and normal surfaces. Transactions of the American Mathematical Society, 360(6), 2849-2866. [More Information]
  • Luo, F., Schleimer, S., Tillmann, S. (2008). Geodesic ideal triangulations exist virtually. Proceedings of the American Mathematical Society, 136(7), 2625-2630. [More Information]
  • Tillmann, S. (2008). Normal surfaces in topologically finite 3-manifolds. L'Enseignement Mathematique, 54(2), 329-380.

2007

  • Chesebro, E., Tillmann, S. (2007). Not all boundary slopes are strongly detected by the character variety. Communications in Analysis and Geometry, 15(4), 695-723.

2005

  • Tillmann, S. (2005). Boundary slopes and the logarithmic limit set. Topology, 44(1), 203-216.

2004

  • Tillmann, S. (2004). Character varieties of mutative 3–manifolds. Algebraic and Geometric Topology, 4, 133-149.

2000

  • Tillmann, S. (2000). On the Kinoshita-Terasaka knot and generalised Conway mutation. Journal of Knot Theory and Its Ramifications, 9(4), 557-575. [More Information]

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