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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



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


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