Connection to the school’s zoom and a greeting word from organizers

Probability on graphs and groups

• Tatiana Nagnibeda (Université de Genève)

Many forms of the Uncertainty Principle

• Eugenia Malinnikova (Stanford University)

Localization for quasiperiodic operators with monotone potentials

• Ilya Kachkovskiy (Michigan State University)

Probability on graphs and groups

• Tatiana Nagnibeda (Université de Genève)

Many forms of the Uncertainty Principle

• Eugenia Malinnikova (Stanford University)

Localization for quasiperiodic operators with monotone potentials

• Ilya Kachkovskiy (Michigan State University)

Probability on graphs and groups

• Tatiana Nagnibeda (Université de Genève)

Many forms of the Uncertainty Principle

• Eugenia Malinnikova (Stanford University)

Localization for quasiperiodic operators with monotone potentials

• Ilya Kachkovskiy (Michigan State University)

Zeroes of sums of eigenfunctions

• Stefano Decio (Norwegian University of Science and Technology)

Some properties of eigenfunctions of the Laplace operator resemble those of trigonometric polynomials. In this light, we will discuss oscillations and zeros for linear combinations of eigenfunctions on Riemannian manifolds. We will prove that zeros are somewhat dense in the manifold and mention some, possibly quite difficult, open questions.

Non-existence of a universal zero entropy system for non-periodic amenable group actions

• Georgii Veprev (Euler Mathematical Institute)

Let $G$ be a non-periodic amenable group. We prove that there does not exist a topological action of $G$ for which the set of ergodic invariant measures coincides with the set of all ergodic measure-theoretic systems of entropy zero. Previously J. Serafin, answering a question by B. Weiss, proved the same for $G=\mathbb{Z}$.

Three Surface Theorems

• Marie Berge Stine (Norwegian University of Science and Technology)

In the 70's Almgren noticed that for a harmonic real-valued function defined on a ball, its L^2-norm over spheres with increasing radius will have an increasing logarithmic derivative with respect to the radius of the mentioned sphere. A similar fact holds true for several other classes of functions which are solutions to PDE's, for example, Helmholtz equation, Schrödinger equation, and elliptic equations. We begin by showing how one can go from harmonic functions to solutions of the Helmholtz equation. Thereafter, we examine similar integrals over a more general class of parameterized surfaces by studying harmonic functions defined on compact subdomains of Riemannian manifolds. Some of the results are joint work with E. Malinnikova.

A Principle of Almost Orthogonality

• Anthony Gauvan (University Paris-Saclay)

In this note, we show that the principle of almost orthogonality proved by Alfonseca, Soria, Vargas remains true in the context of homothecy invariant basis. The same inequality remains true. The proof is based on covering technique and a geometric lemma.

Presentation of master and graduate mathematical educational programs of St.Petersburg University

• Fedor Petrov (St. Petersburg State University)
• Pavel Mozolyako (St.Petersburg State University)

Fourier uniqueness in even dimensions

• Haakan Hedenmalm ( KTH Royal Institute of Technology)

In the work of Radchenko and Viazovska Fourier uniqueness was investigated for test functions in the Schwartz class. The sequences that give uniqueness are square roots of nonnegative integers. Here, we investigate the uniqueness issue for the same sequences but a larger collection of test functions. In addition, an interesting connection with the dynamics of Gauss-type maps is made, by connected the Fourier uniqueness problem for such sequences with the Heisenberg uniqueness pairs problem for the pairs considered by Hedenmalm and Montes-Rodriguez in 2011.

Probability on graphs and groups

• Tatiana Nagnibeda (Université de Genève)

Many forms of the Uncertainty Principle

• Eugenia Malinnikova (Stanford University)

Localization for quasiperiodic operators with monotone potentials

• Ilya Kachkovskiy (Michigan State University)