Jonathan Spreer

Jonathan Spreer is an Associate Professor at the School of Mathematics and Statistics, The University of Sydney, where he has held positions since 2021. His research bridges low-dimensional topology, combinatorics, and parameterized complexity theory, with applications in mathematical software development.

• Education:
  • Doctorate in natural sciences (2011, University of Stuttgart; advisor: Prof. W. Kühnel)
  • Diploma in mathematics and computer science (2008, University of Stuttgart)
  • Maîtrise in mathematics (2007, Université Pierre et Marie Curie)

Research themes include:

• Tight triangulations: Generalizing convexity in discrete geometry, with recent focus on 3- and 4-manifolds.
• 3- and 4-manifold topology: Computational methods for minimal triangulations and crosscap number algorithms.
• Graph-encoded manifolds: Studying combinatorial representations of manifolds via colored graphs.
• Parameterized complexity: Developing efficient algorithms for topological problems under bounded parameters.

Scientific contributions:

• Lead developer of the simpcomp software package for simplicial complex analysis in GAP.
• Key publications on Turaev-Viro invariants, JSJ decomposition complexity, and quantum invariants of 3-manifolds.
• ARC Discovery Project grants for Triangulations: linking geometry and topology with combinatorics (2022) and Trisections, triangulations and the complexity of manifolds (2019).

Teaching and supervision spans computational geometry, topology, and related fields. Current research students include William Hobkirk, Damian Lin, and James Morgan, working on problems in 3-manifold topology and algorithmic complexity.