During the last two decades several remarkable new results were discovered about harmonic measure in the complex plane. This book provides a careful survey of these results and an introduction to the branch of analysis which contains them.  Meer

There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing the Mordell conjecture.  Meer

Discriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry.  Meer

Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings.  Meer

This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples.  Meer

Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole.  Meer

Pseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications.  Meer

Equivariant homotopy theory started from geometrically motivated questions about symmetries of manifolds. Several important equivariant phenomena occur not just for a particular group, but in a uniform way for all groups.  Meer

In this book the author illustrates the power of the theory of subcartesian differential spaces for investigating spaces with singularities. Part I gives a detailed and comprehensive presentation of the theory of differential spaces, including integration of distributions on subcartesian spaces and the structure of stratified spaces.  Meer

Published in two volumes, this is the first book to provide a thorough and systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole.  Meer

An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding.  Meer

An H(b) space is defined as a collection of analytic functions that are in the image of an operator. The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and demanding.  Meer

An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding.  Meer

This book presents a detailed and contemporary account of the classical theory of convergence of semigroups and its more recent development treating the case where the limit semigroup, in contrast to the approximating semigroups, acts merely on a subspace of the original Banach space (this is the case, for example, with singular perturbations).  Meer

Intersection homology is a version of homology theory that extends Poincaré duality and its applications to stratified spaces, such as singular varieties.  Meer

This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classification are equivalent.  Meer

Spectral spaces are a class of topological spaces. They are a tool linking algebraic structures, in a very wide sense, with geometry. They were invented to give a functional representation of Boolean algebras and distributive lattices and subsequently gained great prominence as a consequence of Grothendieck's invention of schemes.  Meer

Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry and topology.  Meer

Graduate students and researchers alike will benefit from this treatment of classical and modern topics in homotopy theory of topological spaces with an emphasis on cubical diagrams.  Meer

This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff.  Meer