Speaker: Taeyong Ahn (KIAS)
Title: Equidistribution for holomorphic endomorphisms of $mathbb{P}^k$
Abstract: In this talk, complex dynamics will be introduced with an equidistribution problem. In particular, we will discuss higher codimensional cases. Let $f:mathbb{P}^ktomathbb{P}^k$ be a holomorphic endomorphism of algebraic degree $d>1$ and $H$ be an analytic subset of $mathbb{P}^k$ of codimension $p>1$. It is expected that for a generic choice of $H$, the sequence ${d^{-np}(f^n)^*[H]}$ of currents of integration converges to the Green $(k-p, k-p)$-current. We will discuss this convergence.

Speaker: Soonjo Hong (NIMS)
Title: Nonhomogeneous equilibrium states in symbolic dynamics
Abstract: Fan and Pollicott developed a theory of dynamics given by nonhomogenoues symbolic spaces and time evolutions. We try to find its application to classical symbolic dynamics, particularly to the research of fibers of measures of shift spaces. (in progess)

Speaker: Sanghoon Kwon (SNU)
Title: Mixing, counting and equidistribution in negatively curved space
Abstract: We review some geometric and dynamical properties of negatively curved spaces; for example, hyperbolic manifolds and R-trees. Especially, we study the thermodynamics and symbolic dynamics to investigate the ergodic theory of geodesic flows and introduce some applications. These will consist of the variational Principle and the counting and equidistribution of orbit points and periods. We also present recent results about the exponential mixing property of geodesic flow in geometrically finite hyperbolic manifolds and graph of groups.

Speaker: Sieye Ryu (NIMS)
Title: Conjugacy invariants of a $D_{infty}$-Markov chain
Abstract: A $D_{infty}$-Markov chain is a topological Markov chain equipped with the action of the infinite dihedral group. We introduce the following conjugacy invariants of $D_{infty}$-Markov chains: $D_{infty}$-SSE ($D_{infty}$-strong shift equivalence), $D_{infty}$-SE ($D_{infty}$-shift equivalence) and the Lind zeta functions. We consider the relationships between these invariants.

Speaker: Youngwhan Son (KIAS)
Title: Uniform distribution and sets of recurrence involving primes
Abstract: We will present new results of equidistribution of sequences involving primes. Also we will discuss some applications of this result to ergodic theory and combinatorics. This is a joint work with V. Bergelson and G. Kolesnik.

Speaker: Jisang Yoo (SNU)
Title: On class maximal measures
Abstract: For a given infinite-to-one factor code $pi$ from a mixing SFT X to Y and an ergodic measure $nu$ on Y of full support, we consider the space of all ergodic invariant measures on X that projects to the given image measure $nu$. We inspect the structure of this space and decompose it into finitely many equivalence classes. Each class contains a unique measure that maximizes entropy.