Focused Workshop on Networks and Their Limits

The workshop is aimed at studying recent advances and open questions of the Beurling theory of arithmetical semigroups.

The goal of this workshop is to investigate the connections between various measurements of complexity of lattices (in topological groups) and their co-volume.

The focused workshop will discuss some recent applications of harmonic analysis methods in fractal geometry. Significant results have recently been achieved in this field, and we would like to better understand some of them through lectures from experts in this field.

The topic of the focused workshop is related to the results and methods of Pablo Shmerkin's 2019 Anals of Maths paper: "On Furstenberg's intersection conjecture, self-similar measures, and the L q norms of convolution"s.

The workshop focuses around the questions of spectral rigidity motivated by the famous question: Can you hear the shape of a drum? Recent progress on dynamical spectral rigidity will be discussed.

The mini workshop focuses on methods for obtaining key estimates on sharp lower bounds for the spectral gap of the finite coordinate processes. These are required for the hydrodynamics limit in several fundamental particle systems or energy exchange systems.