Title: Integrability, Quantization, and Geometry
Subjects: Mathematics, Influence, Algebraic Geometry, Topology, Homology theory, Quantum theory, Influence (Literary, artistic, etc.), Algebraic geometry -- (Co)homology theory [See also 13Dxx] -- Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20], Algebraic geometry -- (Co)homology theory [See also 13Dxx] -- Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38], Algebraic geometry -- Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx] -- Zeta-functions and related questions [See also 11G40] (Birch-Swinnerton-Dyer conjecture), Algebraic geometry -- Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx} -- Families, moduli, classification: algebraic theory, Algebraic geometry -- Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx} -- Mirror symmetry [See also 11G42, 53D37], Algebraic geometry -- Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx} -- Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for, Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Classical differential geometry -- Higher-dimensional and -codimensio, Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx], Algebraic geometry -- Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx} -- Relationships with physics, Associative rings and algebras {For the commutative case, see 13-XX} -- Hopf algebras, quantum groups and related topics -- Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50], Group theory and generalizations -- Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)] -- Ordinary representations and characters, Group theory and generalizations -- Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)] -- Applications of group representations to physics, Convex and discrete geometry -- Discrete geometry -- Lattices and convex bodies in $n$ dimensions [See also 11H06, 11H31, 11P21], Quantum theory -- Quantum field theory; related classical field theories [See also 70Sxx] -- Yang-Mills and other gauge theories [See also 53C07, 58E15], Quantum theory -- Quantum field theory; related classical field theories [See also 70Sxx] -- String and superstring theories; other extended objects (e.g., branes) [See also 83E30], Quantum theory -- Quantum field theory; related classical field theories [See also 70Sxx] -- Two-dimensional field theories, conformal field theories, etc..