# Overview

##### [ Français ]

The goal of the workshop is to gather applied mathematicians, theoretical chemists and physicists, specialists of mathematical and computational methods in relativistic and non-relativistic quantum chemistry and physics, laser physics, cold-matter physics and Bose-Einstein condensates. All these fields of application have in common linear or nonlinear quantum relativistic or non-relativistic wave models, such as the Schroedinger, Gross-Pitaevskii, Klein-Gordon or Dirac equations. The workshop will not only introduce the state-of-the-art in these research fields, but also will address new challenges and the future research trends. The workshop will cover several mathematical areas:

- Numerical and mathematical methods for time dependent linear and nonlinear Dirac and Schroedinger equations.
- Spectral theory applied to quantum Hamiltonians. Spectral pollution. Nonlinear and linear eigenvalue problem for unbounded operators, Dirac operator, Gross-Piatevskii operator. Imaginary time methods, Feit-Fleck exponential method, balanced operators.
- Computational methods for many-body problems. Variational methods.
- Domain decomposition methods, Schwarz waveform relaxation methods, multilevel methods.
- High order operator splitting methods, exponential integrators.
- Multiscale computing in material and cold-matter science.
- High performance computing in quantum and laser physics.
- Application to pair productions, graphene, attosecond science, Bose-Einstein condensate, laser-filamentation, laser-molecule interaction in relativistic regime, quantum imaging, ultrafast laser imaging.