Organisers:
Barbara Dembin (Universite de Strasbourg, France)
Tim Garoni (Monash University)
Stephen Muirhead (Monash University)

Program Description:

This program will bring together researchers working in the closely related fields of percolation theory, spin models, and random height functions to share the latest advances and work collaboratively on open questions. These three fields have been developing in tandem for close to a century, and the many links between them are well-known and frequently exploited.
The aim of this program is to bring together researchers working in these three disciplines, to consolidate these recent advances, and to focus attention on outstanding open questions in the field. The programme will feature several participants who have been instrumental in these recent advances (e.g. Rodriguez, Severo, Nolin, Qian). Major sources of open questions include:

• The properties of the critical phase of percolation and spin models in lower dimensions d ≥ 3, which are mostly wide open despite decades of attempts to connect them to conformal field theories.
• The analysis of critical percolation and spin models in high dimensions, for which the main existing ‘lace expansion’ approach is perturbative and does not permit an analysis down to the critical dimension (c.f. a recent breakthrough in [Duminil-Copin & Panis, preprint, 2024]).
• The study of percolation, spin, and height function models which have non-positive correlations, for which most of the existing techniques break down due to the failure of classical correlation inequalities.

The first week of the programme will be structured, comprising lectures, and the second week will be unstructured, allowing time for collaboration and reflection.

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: 11 July 2027

ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 13 July 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.