Michele Ancona (University of Tel Aviv)

Title: Moments of the number of roots of Kostlan polynomials

Jürgen Angst (Université de Rennes 1)

Title: Almost sure asymptotics for the number of zeros of random trigonometric polynomials.

Abstract: We will explain how variations on the celebrated almost sure CLT by Salem-Zygmund on random trigonometric polynomials allow to deduce the almost sure asymptotics for their number of zeros. This approach is robust enough to be implemented in both independent and dependent frameworks and more generally for random Laplace eigenfunctions on manifolds. This is joint work with G. Poly and T. Pautrel.

Jean-Marc Azaïs (IMT, Université de Toulouse)

Title: Studying the winding number of a Gaussian process: the real method.

Raphaël Butez (Université de Lille)

Title: Outliers for weakly confining Coulomb gases and zeros of random polynomials

Valentina Cammarota (Sapienza University of Rome)

Title: On the correlation between critical points and the critical values for random spherical harmonics

Laure Coutin (IMT, Université de Toulouse)

Title: Donsker theorem in Wasserstein 1 distance and rate of convergence for the number of zeros of random trigonometric polynomials

Federico Dalmao (Universitad de la Republica, Salto)

Title: On the number of roots of random invariant homogeneous polynomials.

Yohann De Castro (Ecole Centrale de Lyon)

Title: Maximum of Gaussian fields on Stiefel manifolds

Céline Delmas (INRAE, Toulouse)

Title: Critical points of isotropic Gaussian fields on the sphere

Vivek Dewan (Université Grenoble-Alpes)

Title: First passage percolation for Gaussian fields

Louis Gass (Université de Rennes 1)

Title: Moments of the number of zeros of non-stationary Gaussian processes.

Damien Gayet (Université Grenoble-Alpes)

Title: Asymptotic topology of random nodal sets

Maxime Ingremeau (Université de Nice Côte d'Azur)

Title: Spectral asymptotics of large quantum graphs

Abstract: Since Weyl’s work a century ago, a lot of papers have studied the asymptotics of the eigenvalues of the Laplacian (in a domain or on a compact manifold) in the limit where the eigenvalues become large. Recently, an other kind of asymptotics has been of interest: consider a sequence of domains, whose size grow to infinity, and count the asymptotic number of eigenvalues of the Laplacian in these domains in a fixed spectral interval. In this talk, we will deal with this kind of asymptotics in the case of quantum graphs (also known as metric graphs), which are just some compact one-dimensional objects where Laplacians can be defined. If time allows it, I will mention analogous results for the scattering resonances of open quantum graphs. Part of this is joint work with N. Anantharaman, M. Sabri and B. Winn

Zakhar Kabluchko (Muenster Universität)

Title: Dynamics of zeroes under repeated differentiation

Raphael Lachieze-Rey (MAP 5, Université de Paris)

Title: Diophantine Gaussian excursions

Antonio Lerario (SISSA, Trieste)

Title: Differential topology of gaussian random fields

Thomas Letendre (IMO, Université Paris-Saclay)

Title: How to resolve the singularities of higher order Kac--Rice densities (in dimension $1$)

Stephen Muirhead (University of Melbourne)

Title: Decay of subcritical connection probabilities for long-range correlated Gaussian fields

Oahn Nguyen (University of Illinois)

Title: The number of limit cycles bifurcating from a randomly perturbed center

Abstract: We consider the average number of limit cycles that bifurcate from a randomly perturbed linear center where the perturbation consists of random (bivariate) polynomials with i.i.d. coefficients. We reduce this problem to the number of real roots of the random polynomial $$f(x) = \sum_{k=0}^{n} k^\rho \xi_k x^k$$ where the $\xi_k$ are independent with mean 0 and variance 1 and $\rho \le -1/2$ is a constant. In earlier work, Do, Vu, and myself established this number for $\rho > -1/2$ via the universality method which naturally breaks down for $\rho \le -1/2$. In this talk, we discuss the solution for the $\rho \le -1/2$. Joint work with Erik Lundberg.

Massimo Notarnicola (Université du Luxembourg)

Title: Geometric functionals of multiple Arithmetic Random Waves, Berry’s Cancellation and Wiener Chaos

Thibault Pautrel (Université de Rennes 1)

Title: Zeros of random trigonometric polynomials with dependent Gaussian coefficients

Giovanni Peccati (Université du Luxembourg)

Title: Local fluctuations of nodal volumes via coupling of Gaussian fields

Hung Viet Pham (Institute of Mathematics, Hanoi)

Title: Conjunction probability of smooth Gaussian fields

Ali Pirhadi (Georgia State University)

Title: Real zeros of random trigonometric polynomials with $\ell$-periodic coefficients

Guillaume Poly (Université de Rennes 1)

Title: Non universality of Fluctuations in Salem-Zygmund CLT

Igor Pritsker (Oklahoma State University)

Title: Real zeros of random orthogonal polynomials.

Lakshmi Priya (Indian Institute of Science)

Title: Overcrowding estimates for the nodal volume of stationary Gaussian processes on $\mathbb R^d$

Andrea Sartori (Tel Aviv University)

Title: Asymptotic nodal length and log-integrability of toral eigenfunctions

Anna-Paola Todino (Politecnico di Torino)

Title: Random Spherical Harmonics: Overview and Recent Results

Hugo Vanneuville (Université Grenoble-Alpes)

Title: An unbounded nodal surface for 3D Bargmann-Fock

Anna Vidotto (U. Chieti-Pescara)

Title: Non-Universal Fluctuations of the Empirical Measure for Isotropic Stationary Fields on $\mathbb{S}^2\times \mathbb{R}$

Igor Wigman (King's College London)

Title: Expected nodal volume for non-Gaussian random band-limited functions

Aaron Yeager (College of Coastal Georgia)

Title: Random polynomials and their zeros

Nadav Yesha (Université de Haifa)

Title: The defect distribution of toral Laplace eigenfunctions via Bourgain's de-randomization