Organisers:
Anthony Conway (University of Texas at Austin)
Diarmuid Crowley (University of Melbourne)
Maggie Miller (University of Texas at Austin)
Mark Powell (University of Glasgow)
Arunima Ray (University of Melbourne)

Program Description:
This workshop will focus on the geometric and algebraic topology of manifolds. The qualitative behaviour of manifolds varies significantly with their dimension. In a sense, dimension four is the boundary case between low and high dimensions; there is enough freedom for the manifold topology to exhibit complex behaviour, but not enough room for the usual high-dimensional tools to work. In particular, there is an astonishing divergence between the smooth and topological settings for 4-manifolds. Moreover, deep questions such as the Poincaré conjecture and the Schoenflies conjecture remain open in dimension four.

Recent years have seen a resurgence of interest in 4-dimensional manifolds, both on the topological side using techniques pioneered by Freedman and Quinn, as well as on the smooth side due to Gabai’s 4-dimensional lightbulb theorem and Watanabe’s disproof of the 4-dimensional Smale conjecture. Notably, this progress can be seen as the result of inspiration drawn both from research on 3-manifolds, including knots and links, as well as on higher-dimensional manifolds. With a new generation of researchers focusing their interest on this area, the time is ripe for new developments.

The aim of this workshop is to bring together junior and senior researchers in 4-manifolds, as well as the neighbouring fields of 3-manifolds and higher-dimensional manifolds, stimulating further collaboration on fundamental questions. In particular, we hope to strengthen the ties between the Australian and international research communities.

Program Structure:

TBD

Registration:

• Deadline: TBD
• Registration is by invitation only. If you are interested to participate in this program, please contact one of the organisers with your CV and research background.
• Arrival date: 10 January 2027

ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 12 January 2027
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.