This volume offers the proceedings from the workshop held at the University of Milan (Italy) on groups of homotopy self-equivalences and related topics. The book comprises the articles relating research on the group of homotopy self-equivalences, homotopy of function spaces, rational homotopy theory, classification of homotopy types, and equivariant homotopy theory.

This volume presents articles from several lectures presented at a conference on Quantum Symmetries in Theoretical Physics and Mathematics held in Bariloche, Argentina. The various lecturers provided significantly different points of view on several aspects of Hopf algebras, quantum group theory, and noncommutative differential geometry, ranging from analysis, geometry, and algebra to physical models, especially in connection with integrable systems and conformal field theories.

This volume presents the proceedings from the AMS-IMS-SIAM Summer Research Conference on Homotopy Methods in Algebraic Topology held at the University of Colorado. The conference coincided with the 60th birthday of J. Peter May. An article is included reflecting his wide-ranging and influential contributions to the subject area. Other articles in the book discuss the Adams $EUL2$ term for elliptic cohomology, mapping class groups and function spaces, rational SO(3) equivariant cohomology theories, toral groups and classifying spaces of $p$-compact groups, dual calculus for functors to...

This volume presents the proceedings from the Colloquium on Quantum Groups and Hopf Algebras held in Cordoba (Argentina) in 1999. The meeting brought together researchers who discussed recent developments in Hopf algebras, one of the most important being the influence of quantum groups. Articles offer introductory expositions and surveys including characteristics of Hopf algebras and their generalizations, biFrobenius algebras, braided Hopf algebras, inner actions and Galois theory, face algebras, and infinitesimal Hopf algebras. The following topics are also covered: existence of integrals,...

Many important problems in applied sciences, mathematics, and engineering can be reduced to matrix problems. Moreover, various applications often introduce a special structure into the corresponding matrices, so that their entries can be described by a certain compact formula. Classic examples include Toeplitz matrices, Hankel matrices, Vandermonde matrices, Cauchy matrices, Pick matrices, Bezoutians, controllability and observability matrices, and others. Structured matrices have been under close study for a long time and in quite diverse (and seemingly unrelated) areas, for example,...

This volume presents the proceedings from the conference on Topology, Geometry, and Algebra: Interactions and New Directions held in honour of R. James Milgram at Stanford University in August 1999. The meeting brought together distinguished researchers from a variety of areas related to algebraic topology and its applications. Papers in the book present a wide range of subjects, reflecting the nature of the conference. Topics include moduli spaces, configuration spaces, surgery theory, homotopy theory, knot theory, group actions, and more. Particular emphasis was given to the breadth of...

This volume contains selected papers that were presented at the AMS-IMS-SIAM Joint Summer Research Conference on Differential Geometric Methods in the Control of Partial Differential Equations, which was held at the University of Colorado in Boulder in June, 1999. The aim of the conference was to explore the infusion of differential-geometric methods into the analysis of control theory of partial differential equations, particularly in the challenging case of variable co-efficients, where the physical characteristics of the medium vary from point to point. While a mutually profitable link has...

This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces,...

This volume presents articles based on the talks at the International Conference on Combinatorial and Computational Algebra. Topics presented here include developments in the following areas: combinatorial and computational aspects of group theory, combinatorial and computational aspects of associative and nonassociative algebras, automorphisms of polynomial algebras and the Jacobian conjecture, and combinatorics and coding theory. This volume aims to serve as an introductory guide for advanced graduate students, as well as a reference source for contemporary researchers in the field.

Hopf algebras have proved to be very interesting structures with connections to various areas of mathematics, particularly through quantum groups. This book presents contemporary research in Hopf algebras.