Younghwan Son

Title: Ergodic sum fluctuations in substitution dynamical systems

Abstract: In this talk we will consider deviation of ergodic sums along fixed points of substitution dynamical systems. Especially, we will present a central limit theorem for noncoboundary eigenfunctions with eigenvalue modulus 1. This is a joint work with E. Paquette.

Antoine Julien

Title: Multiresolution analysis and representations of the dyadic solenoid

Abstract: In this talk, I will present some connections between dyadic wavelets and a well known hyperbolic dynamical system: the dyadic solenoid. More precisely, a wavelet function arising from a multiresolution analysis can be used to define a representation of a C*-algebra associated with the solenoid. Prospectively, I will hint at ways this result could be generalized to "tau-wavelets": a family of wavelets with irrational scaling constant which is defined from the Fibonacci substitution.

Soonjo Hong

Title: Transformation of gibbs measures on shifts of finite type

Abstract: Gibbs states in thermodynamics are expressed as Gibbs measures on shift spaces. We apply the study of the transition classes of factor maps to investigate how Gibbs properties are lost and preserved under factor maps from shifts of finite type.

Jamie Walton

Title: Tools for investigating recurrence properties of polytopal cut and project schemes

Abstract: I will give an overview of the various techniques used to understand how many patches of a certain size may be found in a polytopal cut and project set (its "complexity") and how frequently those patches recur (its "recurrence", or "repetitivity"). In recent work with Henna Koivusalo we defined a new property for polytopal cut and project schemes, the approximately canonical condition, which allows one to replace the analysis of acceptance domains of patches with a simpler analysis via so-called cut regions. I will explain through an example why this property is essentially the minimal one necessary for this purpose by showing that the slightly weaker almost canonical condition, which is in standard usage, does not allow one to directly replace acceptance domains with cut regions. I will go into further detail on why a Diophantine condition for the scheme, in combination with minimal complexity, is necessary and sufficient for the associated cut and project sets to be linearly repetitive.

Sanghoon Kwon

Title: The extreme value distribution of discrete geodesic flows in a quotient of regular trees

Abstract: A logarithm law provides interesting information about a recurrence to shrinking targets in a dynamical systems. Generalizing the logarithm law, we can ask the distribution of extreme values for one parameter actions. In this talk, we discuss the extreme value distribution of discrete time geodesic flows in a quotient of regular trees. This is a joint work with Seonhee Lim.