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research interests of department of mathematics
Research interests of department of mathematics
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 |