Journal of Geometry and Physics

Aims and Scope

Last updating: 28.10.2003

Aims

The purpose of the Journal of Geometry and Physics (JGP) is to stimulate the interaction between geometry and physics by communicating results, ideas and problems between the two areas.

JGP publishes original research articles and review papers interrelating geometry and physics.

Scope

JGP covers the following research topics, with emphasis on the interrelation between geometry and physics:

GEOMETRIC METHODS IN PHYSICS:

• algebraic and differential topology (homology and cohomology, homotopy, fibre spaces, spectral sequences, characteristic classes, foliations, surgery, cobordism, topological groups, Morse theory)
• algebraic geometry (local theory, families and fibrations, curves, surfaces, higher-dimensional varieties, Abelian varieties, algebraic groups, schemes, real algebraic geometry)
• real and complex differential geometry (local/global differential geometry, fibre bundles, connections, Riemannian geometry, Lorentzian geometry, complex manifolds, singularities, potential theory)
• symplectic geometry (symplectic and contact manifolds, Lagrangian submanifolds and Maslov index, Poisson manifolds, canonical transformations, Floer theory, Gromov-Witten invariants, Frobenius manifolds, geometric quantization, deformation quantization, quantization of Poisson manifolds, Lie-Poisson groups)
• global analysis, analysis on manifolds (infinite-dimensional manifolds, nonlinear differential operators, spaces of mappings, variational problems, singularities)
• Lie groups and Lie (super)algebras (Lie groups, Lie algebras, Lie superalgebras, cohomology of Lie algebras, Virasoro and Kac-Moody algebras, vertex algebras)
• supermanifolds and supergroups
• spinors and twistors (Clifford algebras, representations of orthogonal groups, algebraic theory of spinors, spinor bundles, twistor spaces)
• quantum groups (Hopf algebras, quantum groups, deformations of enveloping algebras, Yang-Baxter equations)
• noncommutative topology and geometry (noncommutative topology, differential geometry, algebraic geometry, probability and statistics, dynamical systems)
• geometric control theory
• geometric methods in statistics and probability

CLASSICAL MATHEMATICAL PHYSICS:

• classical mechanics (particle systems, Lagrangian and Hamiltonian mechanics, symmetry and conservation laws)
• dynamical systems (dynamical systems, ergodic theory, Lagrangian and Hamiltonian systems, infinite-dimensional dynamical systems, cellular automata)
• classical integrable systems (integrable PDEs and ODEs, discrete systems, separation of variables, algebraic and geometric techniques, relations with quantum field theory, enumerative geometry, symplectic topology and singularity theory)
• classical field theory (electromagnetism, gauge theories, unified theories, variational approaches, Lagrangian and Hamiltonian approaches, symplectic techniques, symmetries and conservation laws, continuous media)
• general relativity (Einstein equations, exact solutions, unified theories, cosmological models)
• geometric approaches to thermodynamics

QUANTUM MATHEMATICAL PHYSICS:

• quantum mechanics (applications of group theory, techniques of noncommutative geometry and quantum groups, spinors and twistors, geometric quantization, deformation quantization)
• quantum dynamical and integrable systems (relations with quantum groups, quantum separation of variables)
• quantum field theory (Yang-Mills theory, supersymmetric field theories, topological field theories, quantum field theory on curved spacetimes, conformal field theory, statistical field theory, methods from algebraic and differential geometry)
• quantum gravity (quantization of the gravitational field, supergravity)
• strings and superstrings (mirror symmetry, branes, matrix models, relations with algebraic geometry and enumerative problems)

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