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• Selected research projects
• Selected conferences and workshops
• Selected talks (with slides)

Selected research projects

Hyam Rubinstein, Jonathan Spreer, Stephan Tillmann, Trisections, triangulations and the complexity of manifolds, Australian Research Council (ARC) Discovery Project 2019, DP190102259.

Abstract:

Topology is the mathematical study of the shape of spaces such as surfaces and their higher dimensional analogues. Geometry endows these spaces, also called manifolds, with additional properties such as distance, angle and curvature. Manifolds can be studied by decomposing them into simple pieces such as triangles. These triangulations are a very effective tool. Typically the fewer pieces they have, the better they describe their underlying manifold. We develop a new approach based on such small triangulations that aims at practical algorithms for manifolds in dimensions 3 and 4. Concrete aims include connectivity results for triangulations, and algorithms to recognise fundamental topological structures such as trisections and bundles.

Benjamin A. Burton, Jonathan Spreer, Tractable topological computing: Escaping the hardness trap, Australian Research Council (ARC) Discovery Project 2015, DP150104108.

Abstract:

Computational topology is a young and energetic field that uses computers to solve complex geometric problems driven by pure mathematics, and with diverse applications in biology, signal processing and data mining. A major barrier is that many of these problems are thought to be fundamentally and intractably hard. This project will defy such barriers for typical real-world inputs by fusing geometric techniques with technologies from the field of parameterised complexity, creating powerful, practical solutions for these problems. It will shed much-needed light on the vast and puzzling gap between theory and practice, and give researchers fast new software tools for large-scale experimentation and cutting-edge computer proofs.

Benjamin A. Burton, Basudeb Datta, Jonathan Spreer, Nitin Singh, Building triangulations for fast topological computing, DIICCSRTE, Australia-India Strategic Research Fund (AISRF), Round 7, AISRF06660.

Abstract:

Computational topology is a young and fast-growing area of ICT, with roots in geometry and applications in biology, physics, computer vision and cosmology, in which real computations are often prohibitively expensive. We will overcome this by building "tight triangulations", highly efficient forms of input with which we can solve substantial problems cheaply using new and innovative heuristics. Outcomes will include practical software, with significant benefits spanning both ICT and mathematics.

Selected conferences and workshops

Computational & Algorithmic Topology, Sydney (CATS 2020)

This workshop at The University of Sydney will bring together experts and emerging researchers from Australia, the USA and Europe to report on recent results and explore future directions in computational and algorithmic topology and related areas. There will be a focus on problems in computational geometric topology and computational algebraic topology. This workshop aims to stimulate interaction between researchers in order to bring about new collaborations on difficult problems that cannot be tackled from one viewpoint alone.

Organisers:

• Jonathan Spreer (The University of Sydney)
• Stephan Tillmann (The University of Sydney)
• Katharine Turner (Australian National University)

Einstein Workshop Geometric and Topological Combinatorics

This will be a three day workshop on Geometric and Topological Combinatorics, with lectures in the morning and time for discussions and networking in the afternoons. It is primarily funded by the Einstein Foundation Berlin, as part of Francisco Santos' Einstein Visiting Fellowship within the Discrete Geometry Group at FU Berlin for 2016-2019. Additional funding is provided by the project Discretization in Geometry and Dynamics (SFB Transregio 109) and the Berlin Mathematical School.

Organisers:

• Giulia Codenotti (Freie Universität Berlin)
• Jean-Philippe Labbé (Freie Universität Berlin)
• Jorge Alberto Olarte (then Freie Universität Berlin)
• Francisco Santos (Universidad de Cantabria)
• Jonathan Spreer (then Freie Universität Berlin)

Einstein Workshop Discrete Geometry and Topology

This will be a four day workshop with lectures, presentations and informal discussions on discrete geometry and topology, and related topics (combinatorial topology, computational geometry, polytope theory). It is primarily funded by the Einstein Foundation Berlin, as part of Francisco Santos' Einstein Visiting Fellowship at FU Berlin for 2016-2019. Additional funding is provided by the project Discretization in Geometry and Dynamics (SFB Transregio 109) and the Berlin Mathematical School.

Organisers:

• Michael Joswig (Technische Universität Berlin)
• Francisco Santos (Universidad de Cantabria)
• Jonathan Spreer (then Freie Universität Berlin)
• Günter Ziegler (Freie Universität Berlin)

Selected talks (with slides)

Dr Jonathan Spreer   |   The University of Sydney   |   School of Mathematics and Statistics   |   Email: jonathan.spreer@sydney.edu.au