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