# Research Interests

## Analysis of PDEs and harmonic analysis

- PDOs and ΨDOs on curved manifolds and microlocal analysis
- Commutative non-Euclidean Fourier analysis and its relation with quantum integrability
- Non-commutative harmonic analysis and global quantization on groups, homogeneous spaces and more general manifolds
- The correspondence between harmonic analysis and spectral theory
- Harmonic and spectral analysis on almost Abelian groups and homogeneous spaces

## Mathematical physics

- QFT in curved spacetimes and mathematical cosmology
- Elementary particle states in homogeneous cosmological spacetimes
- Quantum integrability and quantization of non-linear systems

## Mathematical statistics and data science

- Mathematical foundations of predictive analytics