The main goal of this conference is to study the recent achievement about algebraic number theory. More precise subjects are as follows.

1. Recent progress on arithmetic on quadratic forms and quadratic polynomials, such as classification and representation problems. Classification of universal and almost universal quadratic forms and quadratic polynomials. Application of various mass formula for quadratic polynomials. Effective determination of representation of quadratic forms and quadratic polynomials and computation of local densities.

2. Automorphic forms and L-functions. θ-lifting and relative trace formula. Arith-metic application of special values of L-function. K-groups of the ring of integers of number fields. Iwasawa theory and BSD conjecture for elliptic curves.

3. Comparison between number fields and the global function fields. Recent progress on arithmetic of global function fields.

4. Integral points and rational points on algebraic varieties. Strong approxima-tion with Brauer-Manin obstruction for Fano varieties. Counting integral points with bounded height by using strong approximation.