This book exposes the connection between the low-dimensional orbifold theory and geometry that was first discovered by Thurston in 1970s providing a key tool in his proof of the hyperbolization of Haken 3-manifolds. Our main aims are to explain most of the topology of orbifolds but to explain the geometric structure theory only for 2-dimensional orbifolds, including their Teichmuller (Fricke) spaces. We tried to collect the theory of orbifolds scattered in various literatures for our purposes. Here, we set out to write down the traditional approach to orbifolds using charts, and we include...
This book exposes the connection between the low-dimensional orbifold theory and geometry that was first discovered by Thurston in 1970s providing a k...
This volume consists of one expository paper and two research papers: T Hirai, A Hora and E Hirai, Introductory expositions on projective representations of groups (referred as E])T Hirai, E Hirai and A Hora, Projective representations and spin characters of complex reflection groups G(m,p,n) and G(m,p,∞), I;T Hirai, A Hora and E Hirai, Projective representations and spin characters of complex reflection groups G(m,p,n) and G(m,p,∞), II, Case of generalized symmetric groups.Since Schur's trilogy on...
This volume consists of one expository paper and two research papers: T Hirai, A Hora and E Hirai, Introductory expositions on projective representati...
This book is a self-contained exposition on the Bohr-Jessen limit theorem. This limit theorem, which is concerned with the behavior of the Riemann zeta function ζ(s) on the line Re s = σ, where 1/2 < σ ≤ 1, was found by Bohr-Jessen in the early 1930s. After Bohr-Jessen, alternative proofs were given by Jessen-Wintner, Borchsenius-Jessen, Laurinčkas, Matsumoto and others. They dealt with this within the framework of probability theory. Their formulation, originated by Jessen-Wintner, is standard nowadays. The present book proposes a new...
This book is a self-contained exposition on the Bohr-Jessen limit theorem. This limit theorem, which is concerned with the behavior of the Riemann zet...
This is a volume of lecture notes based on three series of lectures given by visiting professors of RIMS, Kyoto University during the year-long project 'Discrete Geometric Analysis', which took place in the Japanese academic year 2012-2013. The aim of the project was to make comprehensive research on topics related to discreteness in geometry, analysis and optimization.Discrete geometric analysis is a hybrid field of several traditional disciplines, including graph theory, geometry, discrete group theory, and probability. The name of the area was coined by Toshikazu Sunada, and since being...
This is a volume of lecture notes based on three series of lectures given by visiting professors of RIMS, Kyoto University during the year-long projec...
