Eight expository articles by well-known authors of the theory of Galois groups and fundamental groups focus on recent developments, avoiding classical aspects which have already been described at length in the standard literature. The volume grew from the special semester held at the MSRI in Berkeley in 1999 and many of the new results are due to work accomplished during that program. Among the subjects covered are elliptic surfaces, Grothendieck's anabelian conjecture, fundamental groups of curves and differential Galois theory in positive characteristic. Although the articles contain...
Eight expository articles by well-known authors of the theory of Galois groups and fundamental groups focus on recent developments, avoiding classical...
Random matrices arise from, and have important applications to, number theory, probability, combinatorics, representation theory, quantum mechanics, solid state physics, quantum field theory, quantum gravity, and many other areas of physics and mathematics. This volume of surveys and research results, based largely on lectures given at the Spring 1999 MSRI program of the same name, covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications...
Random matrices arise from, and have important applications to, number theory, probability, combinatorics, representation theory, quantum mechanics, s...
This timely collection of expository papers highlights progress and new directions in Hopf algebras. Arising from the MSRI workshop on Hopf Algebras in October 1999, some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to recent work in quantum groups. In particular, there are articles on recent progress in classifying finite-dimensional Hopf algebras, both in the semisimple case and in the pointed case. The volume also includes an updated version of Mitsuhiro Takeuchi's article "A short course on quantum matrices," now a standard reference...
This timely collection of expository papers highlights progress and new directions in Hopf algebras. Arising from the MSRI workshop on Hopf Algebras i...
This volume contains surveys and research articles by leading experts in several areas of dynamical systems that have recently experienced substantial progress. Some of the major surveys focus on symplectic geometry; smooth rigidity; hyperbolic, parabolic, and symbolic dynamics; and ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this a fascinating look at the state of the art.
This volume contains surveys and research articles by leading experts in several areas of dynamical systems that have recently experienced substantial...
Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists, and systems theorists, their study is now flourishing. This volume, an outgrowth of a 1995 program at the Mathematical Sciences Research Institute, contains expository articles by program participants describing the present state of the art. Here researchers and graduate students will encounter Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects...
Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functio...
This book documents the recent focus on a branch of Riemannian geometry called Comparison Geometry. The simple idea of comparing the geometry of an arbitrary Riemannian manifold with the geometries of constant curvature spaces has seen a tremendous evolution recently. This volume is an up-to-date reflection of the recent development regarding spaces with lower (or two-sided) curvature bounds. The content reflects some of the most exciting activities in comparison geometry during the year and especially of the Mathematical Sciences Research Institute's workshop devoted to the subject. This...
This book documents the recent focus on a branch of Riemannian geometry called Comparison Geometry. The simple idea of comparing the geometry of an ar...
Positivism needs further scrutiny. In recent years, there has been little consensus about the nature of positivism or about the precise forms its influence has taken on psychological theory. One symptom of this lack of clarity has been that ostensibly anti-positivist psychological theorizing is frequently found reproducing one or more distinctively positivist assumptions. The contributors to this volume believe that, while virtually every theoretically engaged psychologist today openly rejects positivism in both its 19th century and 20th century forms, it is indispensable to look at...
Positivism needs further scrutiny. In recent years, there has been little consensus about the nature of positivism or about the precise forms its infl...
This timely collection of expository papers highlights progress and new directions in Hopf algebras. Arising from the MSRI workshop on Hopf Algebras in October 1999, some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to recent work in quantum groups. In particular, there are articles on recent progress in classifying finite-dimensional Hopf algebras, both in the semisimple case and in the pointed case. The volume also includes an updated version of Mitsuhiro Takeuchi's article "A short course on quantum matrices," now a standard reference...
This timely collection of expository papers highlights progress and new directions in Hopf algebras. Arising from the MSRI workshop on Hopf Algebras i...
There have been substantial developments in the mathematical theory of inverse problems over the last twenty years and applications have expanded greatly in medical imaging, geophysical exploration, and non-destructive evaluation. In this book, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in the field, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms.
There have been substantial developments in the mathematical theory of inverse problems over the last twenty years and applications have expanded grea...
