Organisers:
Marco Carfagnini (University of Melbourne)
Pierre Perruchaud (Monash University)
Anna Paola Todino (University Eastern Piedmont, Italy)

Program Description:
This MATRIX programme focuses on the central theme of Gaussian random fields, with an emphasis on the fundamental tools provided by Malliavin calculus and Wiener chaos expansions. These methods have been shown to be extremely powerful in studying fundamental geometric features of excursion sets of given Gaussian fields, including volume, boundary length, and topological invariants like the Euler–Poincaré characteristic.

They are often supplemented by the use of stochastic processes and diffusions on manifolds, a second focal point which will be represented by leading experts. These experts will provide insight into the techniques of spectral analysis, heat kernels and Riemannian geometry.

This one-week workshop is designed to foster national and international collaborations on these topics, by bringing together researchers working at the interface of probability and geometry and by providing the wider probability community with fundamental knowledge of the relevant geometric framework. The programme features two mini-courses on the geometry of random fields and on Gaussian chaos expansions, as well as presentations by early-career participants. Ample time will be dedicated to collaborative work and brainstorming sessions focused on addressing key open questions in the field.

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: 25 June 2028
• Departure date: 30 June 2028

ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 27 June 2028
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.