Contains detailed descriptions of the many exciting developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of research in algebraic combinatorics. This book includes discussions of some topics in the theory of symmet

Based on lectures presented at Pennsylvania State University in February 1987, this work begins with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceeds to the topology and geometry of foliated 3-manifolds. It also explains why four-dimensional space has special attributes.

In this text, the study of torus actions on topological spaces is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and topology. This established link helps in understanding the geometry and topology of a space with torus action by studying the combinatorics of the space of orbits. Conversely, subtle properties of a combinatorial object can be realized by interpreting it as the orbit structure for a proper manifold or as a complex acted on by a torus. The latter can be a symplectic manifold with Hamiltonian torus...

Covers developments in the theory of Teichmuller spaces and offers references to the literature on Teichmuller spaces and quasiconformal mappings. This work describes how quasiconformal mappings have revitalized the subject of complex dynamics. It illustra

This volume addresses algebraic invariants that occur in the confluence of several important areas of mathematics, including number theory, algebra, and arithmetic algebraic geometry. The invariants are analogues for Galois cohomology of the characteristic classes of topology, which have been extremely useful tools in both topology and geometry. It is hoped that these new invariants will prove similarly useful. Early versions of the invariants arose in the attempt to classify the quadratic forms over a given field. The authors are well-known experts in the field. Serre, in particular, is...

Starting from classical arithmetical questions on quadratic forms, this book takes the reader step by step through the connections with lattice sphere packing and covering problems.

An expanded edition of Kac's original introduction to algebraic aspects of conformal field theory which was published by the AMS in 1996. This revised edition is based on courses given by the author at MIT and at Rome University in Spring 1997. New material is added, including the foundations of a rapidly growing area of algebraic conformal theory. Also, in some places, the exposition is significantly simplified.

This volume contains most of the non-standard material necessary to get acquainted with this rapidly developing area. It can be used as an entry point into the study of representations of quantum groups. Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and to apply the theory to representations of Hecke algebras."

This text is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. The book also contains a generous supply of examples and exercises.

Refers to unitary groups of Hilbert spaces, the infinite symmetric group, groups of homeomorphisms of manifolds, and groups of transformations of measure spaces. This book presents an approach to the study of such groups based on ideas from geometric funct