- Evolutions equations in low-dimensional domains;
- Nonlinear wave equations and soliton dynamics;
- Nonlinear waves in cold atoms, BEC and Josephson junctions;
- Spectral theory of Weyl semimetals and Majorana fermions;
- Spectral theory of relativistic quantum mechanical operators;
- Majorana fermions and topological quantum computation;
- Mathematical foundations for non-Hermitian and PT-symmetric physics;
- Quantum networks and graphs.