# research interests of department of mathematics

### *Research interests of department of mathematics*

*Research interests of department of mathematics*

| General, mathematics and education; Numerical mathematics |

| Abstract harmonic analysis |

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

| Homotopy theory; Homotopy groups; Fiber spaces and bundles |

| Modules, bimodules and ideals |

| Mathematical biology in general |

| Existence theories; Optimality conditions |

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

| 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 |

| Polytopes and polyhedral |

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

| 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 |

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

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

| Algebraic structures |

| 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 |

| 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 |

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

| History of mathematics and mathematicians |

| Lie theory and Lie transformation groups |

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

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

| 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 |

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

| Mathematical programming, optimization and variational techniques |

| Operations research and management science; Mathematical programming |

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

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

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

| 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 |