The first Seasonal Institute of the Mathematical Society of Japan (MSJ-SI) “Probabilistic Approach to Geometry” was held at Kyoto University, Japan, on 28th July 2008 - 8th August, 2008. The conference aimed to make interactions between Geometry and Probability Theory and seek for new directions of those research areas. This volume contains the proceedings, selected research articles based on the talks, including survey articles on random groups, rough paths, and heat kernels by the survey lecturers in the conference. The readers will benefit of exploring in this developing...

Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in...

This book is the first volume of the SpringerBriefs in the Mathematics of Materials and provides a comprehensive guide to the interaction of mathematics with materials science. The anterior part of the book describes a selected history of materials science as well as the interaction between mathematics and materials in history. The emergence of materials science was itself a result of an interdisciplinary movement in the 1950s and 1960s. Materials science was formed by the integration of metallurgy, polymer science, ceramics, solid state physics, and related disciplines. We believe that such...

This volume comprises eight papers delivered at the RIMS International Conference "Mathematical Challenges in a New Phase of Materials Science", Kyoto, August 4-8, 2014.

This book introduces the application of computational homology for structural analysis of metallic glasses. The book begins with a brief basic survey of metallic glasses and computational homology, then goes on to the detailed procedures and interpretation of computational homology analysis for metallic glasses.

The book contains a collection of the lectures and talks presented in the Tohoku Forum for Creativity, based on the program of the thematic year in the period of 2014-2016.The main subjects are Noncommutative Geometry and String Theory, including Quantum Field Theory, Poisson Geometry and Deformation Quantization. This book gives an overview of the recent developments in these subjects and thus, to simulate the exchange at new ideas between mathematicians and physicists.