This thematic program will focus on three main themes:

1. Shock Waves in the context of the Euler equations of Hydrodynamics and related models;
2. General Relativity and the mathematics of black holes space-times;
3. Free boundary problems in Life Sciences and Hydrodynamics.

These three themes share a common mathematical base which is the study of nonlinear partial differential equations describing various phenomena arising in hydrodynamics, wave propagation, relativity and life sciences. These include systems of conservation laws, nonlinear waves, free boundary problems and models of mathematical biology. The sharing of ideas and methodology from one field to another as well as the combination of analysis, geometry, mathematical modeling and numerical simulations are central to the study of complex physical systems and to the understanding of important phenomena of nonlinear dynamics, where each approach may provide valuable information.