Geometry and Mathematical Physics

The group works with topics in geometry and analysis that have important applications in mathematical physics, relativity theory and quantum mechanics. 

Group leader: Boris Kruglikov
Fields of research:
Differential Geometry and Lie Theory
  • Symmetry of Geometric Structures
  • Invariants of Lie groups and pseudogroups actions
  • Metric, conformal, projective and general Cartan geometries
Differential Equations and Mathematical Physics
  • Symmetries, differential invariants and equivalence
  • Solvability and integrability of ODEs and PDEs
  • Mathematical Relativity and Quantization theory

Dynamical Systems and Global Analysis

  • Integrable Hamiltonian systems
  • Symmetry methods of solutions
  • Chaotic dynamics and topological entropy