Organisers:
Jessica Purcell (Monash University)
Marc Lackenby (University of Oxford)
Jonathan Spreer (University of Sydney)
Adele Jackson (University of Sydney)

Program Description:
The mathematical study of surfaces and manifolds in dimensions three and four have a rich history of more than a century, dating back at least to Poincaré. One tool that has become increasingly important in their study is that of triangulations and similar decompositions. A manifold is described as a gluing of simpler pieces, such as simplices. The combinatorics and geometry of the decomposition can be used to prove important results about the manifold.

In the 1960s and 1970s Haken used triangulations to consider how surfaces lie in 3-manifolds; applications of his pioneering work continue to produce new insights. In the 1970s and 1980s, following ideas of Thurston, Neumann and Zagier used geometric triangulations to determine hyperbolic-geometric properties of topological Dehn fillings. But the existence in general of geometric triangulations is still unproven. In recent decades, triangulations have become one of the most useful ways to represent 3- and 4-manifolds in computing. This has lead to a more algorithmic study of low-dimensional topology, driven by the combinatorics of triangulations.
As a result, a wealth of new questions and problems have emerged. Examples include open questions on the complexity of 3-manifolds, on effective algorithms for 4-dimensional manifolds, on the search for triangulations that are either good or pathologically bad, etc. There are also open questions about the geometric and topological properties of triangulations, and what geometry implies about the topology, and vice-versa.

The purpose of this workshop is to take a week to bring everyone together, along with Australia’s next generation of researchers in the field, to investigate and tackle these challenges.

Program Structure:

Click here for talk titles and abstracts

Participant list:
Jonathan Spreer (The University of Sydney)
Tejas Kalelkar (Indian Institute of Science Education and Research Pune)
Rhuaidi Burke (The University of Queensland)
Eric Chesebro (University of Montana)
Finn Thompson (The University of Queensland)
Jessica Purcell (Monash University)
William Hobkirk (The University of Sydney)
James Morgan (The University of Sydney)
Emma McQuire (Monash University)
Eric Sedgwick (DePaul University)
Benjamin Burton (The University of Queensland)
Abigail Hollingsworth (University of Warwick)
Connie Hue (Monash University)
Orion Zymaris (Monash University)
Joshua Howie (Monash University)
Vanessa Robins (Research School of Physics, The Australian National University)
Sepehr Saryazdi (University of Sydney)
Lavender Marshall (Monash University)
Daniel Mathews (Monash University)
Elisabetta Matsumoto (Georgia Tech)
Henry Segerman (Oklahoma State University)
Daniele Celoria (University of Queensland)
Justin Lanier (University of Sydney)
Lecheng Su (Monash University)
Alexander Elzenaar (Monash)
Corbin Reid (Monash University)
Arunima Ray (The University of Melbourne)
Stephan Tillmann (The University of Sydney)
Nicola Harif (Monash University)

Registration:

• Registration is now closed
• Arrival date: 1 June 2025
• Departure date: 6 June 2025

ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 3 June 2025
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.