Books in the Advanced Studies in Pure Mathematics series

The conference "Algebraic and Arithmetic Structures of Moduli Spaces" was held in September 2007, at Sapporo (Hokkaido University). Twenty talks were delivered by invited speakers on arithmetic geometry, algebraic geometry and complex geometry. This volume is the proceedings of the conference, to be exact, a collection of eleven papers contributed by some of the speakers which have undergone rigorous refereeing. The topics that are discussed in the articles are diverse in nature such as class field theory, zeta functions, moduli of arithmetic vector bundles, moduli of complex vector bundles, moduli of abelian varieties and theory of display, moduli of Fermat varieties and some topics on cubic threefolds. Among others, the papers of Pappas-Rapoport, Rajan and Weng address many new interesting questions in the related fields, which seem to be worthy of reading for young researchers.

Presents fifteen research papers on various recent topics about multiple zeta-func tions, which include not only multivariate cases but also single-variable cases, additive and multiplicative number theory, as well as poly-Bernoulli numbers and polynomials.

Examines the interactions between geometry and probability theory, and pursues new directions in these research areas. This volume contains the proceedings of a Probabilistic Approach to Geometry conference held in Japan, selected research articles based on the talks, including survey articles on random groups, rough paths, and heat kernels by the survey lecturers at the conference.

A collection of papers from a conference which explored recent developments and interactions in mathematical fields, such as algebraic geometry, integrable systems, Gromov-Witten theory and symplectic geometry and in particular, the developments and interactions coming from ideas in mirror symmetry.

This book is the proceedings of the conference "Arrangements of Hyperplanes" held in August 2009 as the 2nd MSJ-SI (Mathematical Society of Japan Seasonal Institute.) The modern study of arrangements of hyperplanes started in early 1980s. Since the object to study is simple (just a finite set of hyperplanes), there are various mathematical approaches to arrangements including algebra, topology, combinatorics, singularities, integral systems, hypergeometric functions and statistics. Since numerous world-leading experts gave talks in the 2nd MSJ-SI, this book covers many pioneering approaches and new topics in the theory of arrangements as well as indispensable classical results. The book is recommended to any researcher or graduate student who is interested in arrangements of hyerplanes.