Variations On A Theme Of Borel

Explains, using examples, the central role of the fundamental group in the geometry, global analysis, and topology of manifolds.

An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.

The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.

This monograph is the first to present the theory of global attractors of Hamiltonian partial differential equations. A particular focus is placed on the results obtained in the last three decades, with chapters on the global attraction to stationary states, to solitons, and to stationary orbits. The text includes many physically relevant examples and will be of interest to graduate students and researchers in both mathematics and physics. The proofs involve novel applications of methods of harmonic analysis, including Tauberian theorems, Titchmarsh's convolution theorem, and the theory of quasimeasures. As well as the underlying theory, the authors discuss the results of numerical simulations and formulate open problems to prompt further research.

Explores Schrödinger equations with power-type nonlinearity, with scattering results for mass- and energy-critical Schrödinger equations.

The first thorough treatment of the Assouad dimension in fractal geometry, with applications to many fields within pure mathematics.

This concise volume shows how ideas from function and systems theory lead to new insights for noncommutative multivariable operator theory.

Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.