Mathematics of Planet Earth

Modern laser technology allows the generation of ultrafast (few cycle) laser pulses, with intensities exceeding the internal electric field in atoms and molecules, E = 5×10⁹ V/cm, equivalent to the intensity I = 3.5×10¹⁶ Watts/cm². The interaction of such pulses with atoms and molecules leads to new highly nonlinear nonperturbative regimes, where new physical phenomena occur, such as High Harmonic Generation, HHG, from which the shortest pulses have been created, the attosecond pulse (1 asec = 10⁻¹⁸ second, the natural time scale of the electron). One of the major experimental discoveries in this nonlinear nonperturbative regime, the Laser Pulse Filamentation was observed by Mourou and Braun in 1995, as the propagation of pulses over large distances with narrow and intense cones. This has led to intensive investigation in physics and applied mathematics to understand new effects such as self-transformation of these pulses into white light, intensity clamping, multiple filamentation, and to potential applications to wave guide writing, atmospheric remote sensing, lightning guiding and military long range weapons.

The aim of this workshop is to gather mathematicians and physicists specialists of nonlinear optics and filamentation, to try to rigorously derive and analyze relevant non-perturbative models, and to better understand the physics of filamentation.