IS21: Random nodal sets and beyond

date: 7/17/2025, time: 14:00-15:30, room: ICS 139

Organizer: Guillaume Poly & Maurizia Rossi (University Rennes 1 & University Milano-Bicocca)

Chair: Guillaume Poly & Maurizia Rossi (University Rennes 1 & University Milano-Bicocca)

Critical Points and Euler characteristic for Time-Dependent Spherical Random Fields.

Valentina Cammarota (Sapienza University of Rome)

The study of geometric functionals of random fields on manifolds has drawn recently considerable attention. We consider in this talk the fluctuations over time for critical points and Euler characteristic of the excursion sets of general isotropic Gaussian spherical random fields. Critical points of random spherical harmonics and isotropic stationary Gaussian fields are also examples of points process showing a regular structure. We will also present some recent results aimed at quantifying how critical points differ from independently picked points.

Random Scars

Louis Gass (University or Luxembourg)

In this talk, I will present the phenomenon of random quantum scars, which is a strange visual feature (the ‘scars’) dispayed by the isotropic random wave at very large scale, very distinct from the white noise. A parallel will be made between these scars and the notion of quantum scars in quantum mechanics. If time permits, I will present mathematical and numerical challenge concerning the existence and the visualisation of random scars.

Level set percolation of smooth Gaussian fields: an overview

Franco Severo (Université Lyon 1)

Consider the connected components of the level sets of a smooth Gaussian field on the d-dimensional Euclidean space. For which levels does an unbounded connected component appear? When it exists, is it unique? What is the typical size of large bounded components and how does it depend on the level? What happens at the critical level? How do the answers to these questions depend on the dimension? These natural questions lie at the heart of level-set percolation of smooth gaussian fields, a topic that has seen significant progress over the past decade. In this talk, I will give an overview of several recent results in the field and highlight a number of open problems that remain to be addressed.