Mathematics education

General, mathematics and education; Numerical mathematics

Abstract harmonic analysis

Abstract harmonic analysis

Algebraic geometry

Local theory; Homology theory; Special varieties, in particular, varieties defined by ring conditions, and toric varieties; Computational aspects in algebraic geometry

Algebraic topology

Homotopy theory; Homotopy groups; Fiber spaces and bundles

Associative rings and algebras

Modules, bimodules and ideals

Biology and other natural sciences

Mathematical biology in general

Calculus of variations and optimal control; optimization

Existence theories; Optimality conditions

Combinatorics

Designs and configurations; Graph theory; Algebraic combinatorics, in particular, characterization of Cohen-Macaulay simplicial complexes and their generalizations; Extremal combinatorics

Commutative algebra

Theory of modules and ideals; Homological methods; Arithmetic rings and other special rings; Local rings and semilocal rings; Computational aspects and applications; Characterization of Cohen-Macaulay simplicial complexes and their generalizations; Applications of commutative algebra to statistics

Convex and discrete geometry

Polytopes and polyhedral

Differential Geometry

Local differential geometry; Global differential geometry; Non-Euclidean differential geometry; Applications to: game theory, geometric mechanics, and geometric control

Dynamical systems and ergodic theory

Topological dynamics; Smooth dynamical systems; Local and nonlocal bifurcation theory; Random dynamical systems; Finite-dimensional Hamiltonian, Lagrangian, and nonholonomic systems; Applications of dynamical systems in: classical and celestial mechanics, biology, optimization and economics; Approximation methods and numerical treatment of dynamical systems

Functional analysis

Selfadjoint operator algebras; Applications in optimization, convex analysis, mathematical programming, economics

Game theory, economics, social and behavioral sciences

Game theory; Mathematical economics, in particular, applications of statistical and quantum mechanics to economics (econophysics)

General algebraic systems

Algebraic structures

General topology

Connections with other structures, applications: topological dynamics, and transformation groups

Geometry

Real and complex geometry, in particular, hyperbolic and elliptic geometries and generalizations, as well as the theory of polytopes

Global analysis, analysis on manifolds

Infinite-dimensional manifolds; Calculus on manifolds, in particular, real-valued functions; Spaces and manifolds of mappings; Applications to physics; Variational problems in infinite-dimensional spaces

Group theory and generalizations

Abstract finite groups; Structure and classification of infinite or finite groups; Linear algebraic groups and related topics

History and biography

History of mathematics and mathematicians

Lie Groups

Lie theory and Lie transformation groups

Linear and multilinear algebra; matrix theory

Basic linear algebra: Norms of matrices, numerical range, applications of functional analysis to matrix theory

Manifolds and cell complexes

Differential topology; Homology and homotopy of topological groups and related structures

Mechanics of Particles and Systems

Dynamics of a system of particles, including celestial mechanics; Employing tools from: differential geometry, differential topology, Lie theory, functional and variational analysis; Hamiltonian and Lagrangian mechanics; Control of mechanical systems

Number theory

Diophantine equations and approximation, transcendental number theory; Forms and linear algebraic groups; Arithmetic algebraic geometry – Diophantine geometry, specially, elliptic curves over global fields

Numerical analysis

Mathematical programming, optimization and variational techniques

Operations research, mathematical programming

Operations research and management science; Mathematical programming

Operator theory

Special classes of linear operators; Individual linear operators as elements of algebraic systems; Linear spaces and algebras of operators

Ordinary differential equations

Qualitative theory; Geometric methods in differential equations; Control problems; Integral equations

Real functions

Functions of several variables, in particular, calculus of vector functions

Systems theory; control

Controllability, observability, and system structure; Control systems, in particular, non-linear systems, systems governed by ordinary differential equations, adaptive control, and control problems involving computers; Stability, in particular, stabilization of systems by feedback, and adaptive or robust stabilization