Transfer operators of analytic hyperbolic dynamical systems
In a seminal paper Ruelle showed that the long time asymptotic behaviour of analytic hyperbolic dynamical systems can be understood in terms of the eigenvalues, also known as Pollicott-Ruelle resonances, of the so-called transfer operator, a compact operator acting on a suitable Banach space of holomorphic functions. This talk will be a gentle introduction to this fascinating topic and set the scene for the following talk by Julia Slipantschuk.

Stochastic properties of power grid dynamics
Multiple types of fluctuations impact the collective dynamics of power grids and thus challenge their robust operation. Fluctuations result from processes as different as dynamically changing demands, energy trading and an increasing share of renewable power feed-in. Here we analyse principles underlying the dynamics and statistics of power grid frequency fluctuations. Considering frequency time series for a range of power grids, including grids in North America, Japan and Europe, we find a strong deviation from Gaussianity, and a need for new stochastic modelling approaches.

Topological methods for symbolic discrepancy
We discuss in this lecture the notion of bounded symbolic discrepancy for subshifts from a topological dynamics viewpoint. Bounded discrepancy provides particularly strong convergence properties of ergodic sums toward frequencies. It is also closely related to the notions of balance in word combinatorics and of bounded remainder set. We focus on three families of shifts, namely hypercubic, substitutive and dendric shifts. For this latter family, we study and rely on their dimension group, providing necessary and sufficient conditions for two dendric subshifts to be (strong) orbit equivalent.

Langevin equations with non-Markovian and non-Gaussian noise
I will try to make this talk as approachable and fun as possible :). See details here.

Tiling spaces and their dynamics
In this talk we will explain how one can study aperiodic tilings and their associated aperiodic order by introducing a dynamical system on related spaces, and we will give an overview of results in the area.

Large deviation perspective on the "efficiency" of reset processes
Reset processes are stochastic processes which randomly reset at some time to their initial condition. They have attracted much interest in the nonequilibrium statistical physics community in the last few years, and many results concerning the appearance of nonequilibrium steady states have been found. We focus on studying large deviations of a particular observable associated to a discrete reset process: the ratio between current and number of reset steps, which can be regarded as a form of efficiency. We discuss its large deviation shape, and present some open questions related to the appearance of a change of scaling in the underlying process.

Anomalous diffusion in stochastic, biological and random dynamical systems
I will present a simple model of a so-called random dynamical system that randomly mixes in time chaotic dynamics generating normal diffusion with non-chaotic motion where all particles localize. Varying a control parameter the mixed system exhibits a transition characterised by subdiffusion, ageing and weak ergodicity breaking. I may also give a brief outline of some of my other projects on anomalous diffusion in stochastic and biological systems.

Universal statistics of records
Records are rather common in everyday life: we are always talking of record rainfall, record temperature, records in sports and stock prices etc. A natural question is: How many records occur in a typical time-series of length n? It turns out that in many natural time-series, the average number of records grow universally with n! Where does this universality come from? In this talk, I will first make a broad review of record statistics, with emphasis on its universal aspects. Later I’ll discuss a realistic, yet exactly solvable record model for rainfall, where the presence of dry days induces negative correlations between record-beaking precipitation events.

Anomalous statistics of extreme random processesUniversal Statistics of Records
I am going to discuss two problems of extremal statistics in which unusual (but related to each other) features arise: a) statistics of two-dimensional "stretched" random walks over a semicircle with Kardar-Parisi-Zhang (KPZ) scaling, b) spectral properties of symmetric tridiagonal random matrices (operators) whose off-diagonal elements can independently take values 0 and 1. The spectral density of the ensemble of such random matrices has a specific fractal (ultrametric) structure. In the spectral statistics of such random matrices the Lobachevsky's geometry and the elements of number theory related to the theory of modular forms emerge. The edge of the spectral density of such matrices has a "Lifshitz tail", typical for the one-dimensional Anderson localization. I will show that the "Lifshitz tail" can be considered as the manifestation of KPZ scaling and statistics of large deviations. I expect also to highlight a relationship of the spectral properties of symmetric tridiagonal random matrices with the "phyllotaxis" (emergence of Fibonacci sequences in nature).

Blaschke products and their transfer operators
In this talk I will survey recent work with Oscar Bandtlow and Wolfram Just on how to exploit rich analytic structure of Blaschke products to construct expanding circle maps and hyperbolic Anosov diffeomorphisms on the torus with explicitly computable non-trivial Pollicott-Ruelle resonances.

On the special adsorption transition of interacting self-avoiding trails in two dimensions
We investigate the surface adsorption transition of interacting self-avoiding square lattice trails onto a straight boundary line. The character of this adsorption transition depends on the strength of the bulk interaction, which induces a collapse transition of the trails from a swollen to a collapsed phase, separated by a critical state. If the trail is in the critical state, the universality class of the adsorption transition changes; this is known as the special adsorption point. Using FlatPERM, a stochastic growth Monte Carlo algorithm, we simulate the adsorption of self-avoiding interacting trails on the square lattice using three different boundary scenarios which differ with respect to the orientation of the boundary and the type of surface interaction. We confirm the expected phase diagram, showing swollen, collapsed, and adsorbed phases in all three scenarios, and confirm the universality of the normal adsorption transition at low values of the bulk interaction strength. Intriguingly, we cannot confirm the universality of the special adsorption transition. In particular, we find two different values for the associated crossover exponent.

Example of nitric oxide and nitrogen dioxide levels in areas of Greater London
My talk will be an introduction into Superstatistics, which can be thought of as "a statistics of a statistics". Basically, in the real world, physical systems are rarely described by an equilibrium statistics. This approach takes a physical system, breaks it down into superimposed equilibrium statistics. A temperature is taken at each of these smaller intervals, which helps to describe the statistics of the greater system. Following my introduction, and some basic derivations, I will speak about my current work with superstatistics – specifically, using superstatistics to explain the distributions of nitric oxide and nitrogen dioxide levels at locations around London.

Density evolution under a chaotic dynamical system – eigenfunctions of the Perron-Frobenius (PF) operator for the Nth-order Tschebyscheff maps
As chaotic systems are extremely sensitive to initial conditions, study of an individual trajectory requires infinite precision on the initial point. Instead we investigate such a system starting with an ensemble of points characterised by a probability density function. The Perron-Frobenius (PF) operator is thus defined for evolution of densities where the natural invariant density as a fixed point of the operator. In this talk I will start with simple piecewise-linear full-branch maps such as Bernoulli shifts and the tent map, study their eigenfunctions of the PF operator and then by topological conjugation, we find eigenfunctions for the Nth-Tschebyscheff maps. If time permits, I will also briefly talk about our next step of coupling chaotic maps on a discrete lattice.

On moving frames and quantum ribbons
We introduce the concept of moving frames and where to use them, followed by the notion of a quantum ribbon (in arbitrary dimensions) along with the definition of the corresponding quantum Hamiltonian on such strip. Localization of essential spectrum for asymptotically flat strips, the existence of bound states in purely bent strips and Hardy inequalities for twisted strips will be presented, and more importantly, explained. Last but not least, the spectrum of the Möbius strip will be tackled in three different models both analytically and numerically, with comparisons of the results.