Geometry, Algebraic Differentiable dynamical systems Calabi-Yau manifolds Curves, Algebraic Elliptic space Fourier transformations Jacobians Mathematical physics Mathematics Quantum groups Quantum theory Relativity and gravitational theory -- Unified, higher-dimensional and super field theories -- String and superstring theories Torus (Geometry) $K$-theory Algebraic geometry Algebraic geometry -- (Co)homology theory -- Sheaves, derived categories of sheaves and related constructions Algebraic geometry -- Families, fibrations -- Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) Algebraic geometry -- Special varieties -- Supervarieties Algebraic geometry -- Surfaces and higher-dimensional varieties -- $K3$ surfaces and Enriques surfaces Category theory; homological algebra Differential geometry Differential geometry -- Symplectic geometry, contact geometry -- Generalized geometries (à la Hitchin) Global analysis, analysis on manifolds Hodge theory Manifolds and cell complexes -- Low-dimensional topology -- Invariants of knots and 3-manifolds Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Polylogarithms and relations with $K$-theory Quantum field theory Quantum theory -- Quantum field theory; related classical field theories -- Quantum field theory; related classical field theories Quantum theory -- Quantum field theory; related classical field theories -- Two-dimensional field theories, conformal field theories, etc Relativity and gravitational theory -- Unified, higher-dimensional and super field theories -- Unified, higher-dimensional and super field theories