Geometry, topology and mathematics teaching methodology department

Description

Head of Department: Professor, Academician, D.Sc. in Physics and Mathematics – Vyacheslav I. Yanchevsky

Department staff: 2 Professors, 6 Associate professors, 3 Senior Lecturers

Specializations

  • geometry and topology;
  • methods of teaching mathematics.

The main topics for special courses

  • Brauer groups of algebraic varieties and schemes;
  • Differential-geometric structures on smooth manifolds;
  • Lie groups and Lie algebras;
  • Compact transformation groups, theory of refracts and extensors;
  • Smooth manifolds and fibre bundles;
  • Homogeneous spaces of Lie groups;
  • Invariant structures on homogeneous manifolds;
  • Generalized symmetric spaces;
  • Structures and constructions of topological spaces;
  • Methods of teaching mathematics.

Research directions

  • Geometry and arithmetic of algebraic varieties and applications to algebraic K-theory;
  • Geometric topology; extensor theory of transformation groups;
  • Invariant structures on homogeneous spaces of Lie groups;
  • Generalized symmetric spaces;
  • Generalized Hermitian geometry;
  • Structures and constructions of topological spaces.