This book contains papers presented at the 1993 Como meeting on groups of Lie type and their geometries. Themes represented here include: subgroups of finite and algebraic groups, buildings and other geometries associated to groups of Lie type or Coxeter groups, generation, and applications. This book will be a necessary addition to the library of all researchers in group theory and related areas.

This monograph covers Poisson-Szego integrals on the ball, the Green's function for DEGREESD*D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. It also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Greens potentials. Applications of some of the results to Hp spaces, and...

The theory of these modules together with their bounded and unbounded operators is not only rich and attractive in its own right but forms an infrastructure for some of the most important research topics in operator algebra. This book provides a clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material. Graduate students and researchers working in operator algebras will welcome this book as an excellent resource.

The number theoretic properties of curves of genus 2 are attracting increasing attention. This book provides new insights into this subject; much of the material here is entirely new, and none has appeared in book form before. The authors include an explicit treatment of the Jacobian, which throws new light onto the geometry of the Kummer surface. Mathematicians can then determine the Mordell-Weil group for many curves, and in many nontrivial cases they can find all rational points. The results exemplify the power of computer algebra in diophantine contexts, but computer expertise is not...

This study is concerned with computing the homotopy classes of maps algebraically and determining the law of composition for such maps. The problem is solved by introducing new algebraic models of a 4-manifold. Including a complete list of references for the text, the book appeals to researchers and graduate students in topology and algebra.

This collection of survey papers by leading researchers in ergodic theory and low-dimensional and topological dynamics comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one...

Concerned with two fundamental problems in low-dimensional topology, the D(2)-problem and the realization problem, F.E.A. Johnson develops general methods and provides complete solutions in some instances. His book is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field.

After describing the module-theoretic aspects of coalgebras over commutative rings, this volume defines corings as coalgebras for non-commutative rings. Topics covered include module-theoretic aspects of corings (such as the relation of comodules to special subcategories of modules: sigma-type categories); connections between corings and extensions of rings; properties of new examples of corings associated to entwining structures; generalizations of bialgebras such as bialgebroids and weak bialgebras; and the appearance of corings in non-commutative geometry.

The British Combinatorial Conference attracts a large following from the U.K. and international research community. Held at the University of Wales, Bangor, in 2003, the speakers included renowned experts on topics currently attracting significant research interest, as well as less traditional areas such as the combinatorics of protecting digital content. All the contributions are survey papers presenting an overview of the state of the art in a particular area.

The Foundations of Computational Mathematics meetings serve as a platform for cross-fertilization between numerical analysis, mathematics and computer science. This volume contains the invited presentations given by some of the leading authorities in the world. Topics surveyed range from partial differential equations to image processing, biology, complexity, number theory and algebraic geometry.