Main lines of research are:

Functional analysis Differential Geometry Differential Equations and Numerical Analysis Statistics and Operational Research  Algebra
Banach space geometry and operator theory Geometric Analysis

(problems associated with the mean curvature, conformal and complex geometry, geometric flows)

Non-local PDE for particle systems: analysis and accelerated numerical simulation Gaussian random fields and Gamma correlated Semigroups
  Semi-Riemannian Geometry and Relativity Variational Methods and Elliptical PDE of Mathematical Physics Stochastic modeling of tumor growth Coding Theory and Cryptography
  Global Geometry of Surfaces and Associated Nonlinear Equations Orthogonal polynomials Web surveys and smartphones
  Dynamics of complex systems
  Functional data analysis