Nhan Phu Chung (Sungkyunkwan University)

- Title : Livsic theory for group actions.

- Abstract : In this talk, we will present Livsic theory of continuous (Holder) cocycles for group actions. In contrast to the map case, when the acting groups are higher rank, for certain systems we always have cocycle superrigidity without any assumptions of cocycles on periodic data. This is mainly joint work with Yongle Jiang.

Soonjo Hong (Hongik University)

- Title : Markov approximation of $g$-measures in projective metric

- Abstract : Markov measures are known to be dense in the set of probability measures on a compact metric spaces, in the vague topology. We introduce projective metric between the probability measures on a one-dimensional shift space and the topology it induces. The projective topology is stronger than the vague topology. Also we see that the canonical Markov approximation of a $g$-measure converges to the measure in the projective topology.

In-Jee Jeong (KIAS)

- Title : Renormalization in Polygon Exchange Transformations

- Abstract : The renormalization scheme is an essential tool for understanding polygonal exchange transformations, which are two-dimensional analogues for interval exchange transformations. By means of several examples, we demonstrate how the renormalization procedure helps one to understand the dynamics of such maps. These examples will be taken from works of S. Tabachnikov, R. Schwartz, P. Hooper, and others

SunHo Kim (Ajou University)

- Title : An introduction to Cuntz-Krieger algebras

- Abstract : Much research has been carried out on the relationship between symbolic dynamics and C*-algebras. In 1980, Cuntz and Krieger introduced a class of C*-algebras associated to finite matrices, or equivalently, to graphs. This class of C*-algebras, so called Cuntz-Krieger algebras, contains important classes (for example, Cuntz algebras, Toeplitz algebras, and all AF-algebras up to Morita equivalence) and has a beautiful interplay between visual properties of the graph and algebraic properties of the corresponding C*-algebra. In this talk, I will briefly review the definition of a C*-algebra and its representation and introduce generalized versions of Cuntz-Krieger algebras.

Sanghoon Kwon (KIAS)

- Title : Lyapunov exponents and SRB measure for hyperbolic flows

- Abstract : We review Lyapunov exponents and Sinai-Ruelle-Bowen measure for hyperbolic flows. Our aim is to investigate the measure-theoretic entropy of geodesic flows on compact strictly convex projective surface, with respect to Sinai-Ruelle-Bowen measure. If time permits, we will discuss a symbolic dynamical system for hyperbolic flows, developed by Rufus Bowen.

Jungyup Lee (Catholic Kwandong University)

- Title : Substitution tilings without finite local complexity

- Abstract : For the study of discrete spectrum on dynamical systems, a lot of study has been done on tilings which have finite local complexity(FLC). However not much is known for the case of tilings without FLC. So we visit substitution tilings without FLC for various properties of dynamical spectrum. We first show that if substitution tilings have uniform patch frequencies, then the dynamical systems generated by the substitution tilings are uniquely ergodic. We also give a characterizing property for an eigenvalue of the dynamical systems. From this, we can provide a few equivalent properties for dynamical systems to be not weakly mixing. This is a joint work with Boris Solomyak.

Jumi Oh (Sungkyunkwan University)

- Title : Expansive Dynamical Systems fromMeasure Theoretical Viewpoint

- Abstract : Hyperbolic dynamical systems are nowadays fairly understood from the topological and ergodic point of view. In this talk, we discuss some recent and ongoing works on the dynamics beyond hyperbolicity from measure theoretical viewpoint. More precisely, we focus on the subdynamics, homoclinic classes, with the measure theoretic expansiveness.

Younghwan Son (POSTECH)

- Title : Recurrence and ergodic average

- Abstract : The ergodic method initiated by Furstenberg provided the connection between recurrence properties of dynamical systems and combinatorics. In the first talk we will survey some results on the limiting behavior of ergodic averages and recurrence results, which are related to combinatorial results such as Szemeredi theorem and Sarkozy theorem. In the second talk, we will discuss some results on joint ergodicity, which is a generalization of ergodicity of multiple ergodic averages.

Jisang Yoo (Sungkyunkwan University)

- Title : Equilibrium states and relative equilibrium states

- Abstract : We first review the theory of measures of maximal entropy and equilibrium states on expansive systems with specification properties.

We recall earlier results and new results on the structure of an arbitrary factor map $pi:X to Y$ between symbolic dynamical systems.

Combining these, we show that any sufficiently regular equilibrium state $nu$ on $Y$ lifts to a unique measure of maximal relative entropy on $X$. This answers a question raised by Boyle and Petersen (for lifts of Markov measures) and generalizes the earlier known special case of finite-to-one factor codes.