Description

The similarity between the geometry of finite-dimensional spaces and the properties of function spaces (such as that between the theory of Fourier series and studies of Cartesian orthogonal coordinates) is so extensive that its development was called the "Functional Analysis" in the beginning of the 20th century.

 Today this enormous part of mathematics and physics (which provided, for instance, the basis for quantum mechanics, constructed as the geometry of spaces of functions which describe the states of physical systems) is one of the most important domains both of fundamental science and its applications to natural sciences.

Among these applications especially important are those to topology and the global geometry of manifolds, including the creation of the mathematical patterns of quantum field theory and of related objects such as manifolds and vector fields, connections, symplectic and contact structures, knots and braids, wave fronts and caustic surfaces of geometric optics, and so on.

The Journal is devoted to Functional Analysis in this wide sense, including calculus on manifolds and singularity theory; global variational calculus and the study of topological invariants of algebraic and number-theoretic objects; theories of attractors and bifurcations of dynamical systems; geometries of Lagrangian and Legendrian submanifolds in symplectic and contact topologies; physical applications of Lie algebras; cohomologies; algebraic geometry (both complex and real); mixed Hodge structures and theories of Newton polyhedra (with their applications to mixed volumes, to fewnomials, and to systems of partial differential equations and their Pfaffian systems).