This workshop brings together dynamicists who use techniques from, and are motivated by, combinatorics, geometry, and number theory.  The topics cover a broad swath of dynamics, including ergodic theory, homogeneous dynamics, symbolic dynamics, Teichmuller theory, and billiards, and the aim of the workshop is to highlight the common features across these subjects.

A abstract measure-preserving system consists of a space with a discrete-time dynamics and a time-invariant probability distribution. Such systems provide the broadest setting for asking: What kinds of long-run randomness can be generated by dynamics? This is the province of ergodic theory.

The most thorough kind of answer to ...

This conference is aimed towards both complex and real dynamics. The idea is to connect different techniques from several fields of mostly low-dimensional dynamics. While complex analytic maps are quite rigid in comparision to other families of maps often studied, perturbing such maps in an non-rigid way has shown to be of extreme importance ...

It has been known that simple dynamical systems can give rise to chaotic behavior, with fractal invariant sets and that in their parameter space, the bifurcation locus (where the dynamics changes) also becomes a fractal set. The self-similarity in the phase space can be explained by the dynamics itself, ...

Functional data such as space curves, images, and surfaces are seldom sensed directly; curves are often noisily and discretely sampled, images are subject to blurring and deformation, and surfaces are often obtained via indirect linear measurements. Understanding the generation of the observations then requires modelling the act of acquisition, and ...

Spatio-temporal modelling central to many modern applications, but the dimensionality of the domain of such data poses both conceptual and computational statistical challenges. These are exacerbated in a nonparametric setting, where questions related to asymptotic framework and invariance assumptions arise. The areas of functional data analysis and random field analysis ...

In classical papers, Iso Schoenberg (1938, 1942) laid the ground for the study of isotropic positive definite functions on Euclidean spaces and spheres, respectively. Subsequently, positive definite functions on Euclidean spaces have been studied extensively in spatial statistics and related fields. In contrast, positive definite functions on spheres ...

Topological and discrete data such as trees and networks constitute strongly non-Euclidean structures, often beyond the reach of traditional statistical tools. Their analysis is often challenged by computational tractability, as natural constraints such as permutation invariance are computationally hard to implement. Still, such data can be often transposed into more ...

Optimal transport has a long standing history in different branches of science, originating from physics and logistics. Since its emergence as a rigorous mathematical concept in the last century it has influenced and shaped various areas within mathematics but it also has been proven to a be a remarkably rich ...

All information including the speakers and the confirmation of the school dates within the 8 to 12 June 2020 week will soon be announced.

Important classes of functional data, such as random measures and random operators, are intrinsically constrained and need to be represented as elements of suitable non-Euclidean spaces, such as Hilbert manifolds. The interplay between the infinite dimensionality of their variation and the non-linearity of their representation space poses novel challenges for ...

TBA

This workshop is concerned both with the structure theory of locally compact groups acting on discrete structures, and various notions of self-similarity as seen e.g. in Grigorchuk's and Sidki's groups. A crucial link between the two subjects stems from Baumgartner-Willis' tree representation theorem which associates a self-similar group acting on ...

I will begin by giving an introduction to self-similar groups and their role in modern mathematics. This will in particular require appearance of finite automata and automatically generated sequences, Cantor systems and minimal sushifts of the Bernoulli shift.

Then I will explain the role of Bernoulli measures in the dynamics ...

This conference contains contributions that give an overview of the current research in geometric mechanics. This scientific subject is simultaneously close to mathematics, physics, and engineering and its general philosophy consists in taking advantage of fruitful interactions between geometry on the one hand and dynamics and mechanics on the other. ...

A powerful theme in the structure theory of locally compact groups is that ‘local’ properties of the group can have ‘global’ implications for the structure of the group. A classical example is given by Lie groups and their locally defined Lie algebras. In this workshop we explore local-to-global mechanisms for ...

TBA

T.d.l.c. groups can generally be realised as groups of isometries of locally finite connected graphs, and this viewpoint brings geometry to the investigation of t.d.l.c. groups. Not only are isometry groups of trees and buildings key examples of t.d.l.c. groups, but general results about group structure are related to global ...

TBA

Transfer operators have been used to study rare and extreme events in dynamical systems and the linear - or nonlinear - response of systems to perturbations, including applications to climate dynamics.

This conference brings together experts from both theoretical and applied aspects of these studies, also in ...

This school will provide courses from experts on several aspects of the spectrum of transfer operators. Special attention will be provided to the theory of anisotropic spaces, and to applications in geometrical or physical settings.

The target audience includes PhD students and young postdocs. We plan 3 or 4 minicourses and ...

This conference brings together experts who study Ruelle-Pollicott resonances by using semiclassical and dynamical approaches.

Topics range from the Fried conjectures and other geometrical conjectures to various approaches to construct anisotropic spaces and strategies to obtain spectral gaps and essential spectral gaps, including the fractal uncertainty principle, and addressing non ...

There has recently been an explosion of results about transfer operators acting on anisotropic Banach spaces, starting with correlation decay and the analyticity properties of the Ruelle dynamical zeta function of uniformly hyperbolic maps and flows. These techniques have been extended to hyperbolic systems withsingularities, but the results there ...