The research of the group members includes the following branches of Global Analysis:
- Global Variational Analysis (variational theory on fibered spaces, spaces with structure group, invariance and symmetry transformations, variational sequences, extensions to higher order Grassmann bundles)
- Differential Equations on Manifolds (variational and non-variational differential equations, differential constraints, invariance and conservation laws, Hamilton theory and its generalizations, non-holonomic constraints)
- Differential Invariants and Natural Lagrange Structures (classification of invariant geometric objects, jets and contact elements, properties of differential invariants)
- Geometric Methods in Physics (variational principles, natural variational principles, energy-momentum tensors)