- Geometric Analysis on Manifolds
- Elliptic Partial Differential Operators on Manifolds
- Heat Equation Methods; Heat Kernel Asymptotics
- Spectral Asymptotics; Spectral Geometry
- Spectral Determinants and Zeta functions
- Boundary Value Problems; Oblique and Discontinuous Boundary Value Problems
- Mathematical Physics
- Completely Integrable Systems; Korteweg-de Vries hierarchy
- Equations of Mathematical Physics
- Quantum Field Theory, Quantum Gravity and Gauge Theories
- Quantum Field Theory in Curved Space-time
- Higher-derivative Quantum Gravity
- Non-perturbative Aspects of Yang-Mills Theory
- Higher Spin Fields on Curved Manifolds
- String Theory
- Differential Geometry
- Symmetric Spaces
- Kähler Manifolds
- Spaces of Riemannian Metrics on Manifolds
- Financial Mathematics