Symbolic dynamics, a part of discrete dynamical systems, is the study of spaces consisting of infinite arrays defined by certain constraints on finite subsets. A rich theory has been developed on 1-dimensional symbolic dynamics in the last several decades, but the higher-dimensional case is more problematic and many problems occurring in multidimensional symbolic dynamics involve computability issues. In this talk, an introduction to the theory of multidimensional symbolic dynamics and the basic notion of the theory of computation will be presented. In the second part of the talk, we will see why computability problems are crucial for the development of the theory in the multidimensional actions.

Propensity score adjustment is a popular technique for handling unit nonresponse in samplesurveys. If the response probability depends on the study variable that is subject to missingness, estimating the response probability often relies on additional distributional assumptions about the study variable. Instead of making fully parametric assumptions about the population distribution of the study variable and the response mechanism, we propose a new approach of maximum likelihood estimation that is based on the distributional assumptions of the observed part of the sample. Since the model for the observed part of the sample can be verified from the data, the proposed method is less sensitive to failure of the assumed model of the outcomes. Generalized method of moments can be used to improve the efficiency of the proposed estimator. Results from a limited simulation study are presented to compare the performance of the proposed method with the existing methods. We also present an application of the proposed method to the exit poll for the 19th legislative election in Korea.

 The higher Chow group is introduced by S. Bloch, which satisfies localization long exact sequence extending the classical Chow group. It is also related to arithmetic questions such as the special value of L-functions.  It is interesting question to find varieties with big higher Chow group. In this talk, we construct surfaces over the formal Laurent series field over C, with big higher Chow group. We use the etale cycle map c(X) and the monodromy weight  spectral sequence to compute the lower bound of  dim(Im(c(X))).

In the theory of elliptic P.D.E.'s, an overdetermined problem is one where both the Dirichlet and Neumann boundary values are prescribed. This puts strong geometric constraints on the domain. A famous result of J. Serrin asserts that if is a bounded domain D in R^n which admits a function u solution of ꠑ Delta u =-1 in D with zero Dirichlet boundary value and constant Neumann boundary values, then D is a ball. The boundary of D is then a sphere, a constant mean curvature. I will present other similar results and in particular the existence of a 1-to-1 correspondence between harmonic functions which solve an overdetermined problem and a certain type of minimal surfaces.