Mathematical and numerical analysis for quantum wave equations: from theory to applications

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This applied mathematics research program is highly motivated by strong field laser physics and Quantum ElectroDynamics (QED), which are very dynamic and fast evolving research fields in theoretical and applied physics. The latter are also the source of many current and future applications. They have even led to the birth of a new science, the celebrated Attosecond Science, dedicated to the control of electron dynamics in atoms and molecules, using ultrashort and intense laser pulses! Canada is a leader in those fields, and this research proposal intends to contribute and to strengthen their development from the mathematical and computational point of view. Indeed, the highly nonlinear and complex phenomena occurring in photonics, nonperturbative nonlinear optics, and QED require advanced and modern mathematical models and tools for their analysis, and the development of efficient and accurate computational methods for their approximation and simulation. Although the program will mainly focus on mathematical, numerical and modelling aspects, simulation codes will be also developed/improved and applications in fundamental and applied physics will be explored within interdisciplinary collaborations.