The aim of this conference is to invite recognized experts to present recent advances on a certain number of themes in the field of nonlinear PDEs and their applications, as well as to encourage the interactions of the speakers with researchers working in this field at Paris 13 University. The presentations will cover both theoretical aspects (qualitative analysis of the equations) and applied aspects (modeling, physical or biological interpretation of the results of the qualitative and / or numerical study of the model). \\ The timetable will be organized so as to provide important time slots for discussions and collaborations by small groups. Doctoral students and post-doctoral students will profitably attend the presentations. The themes selected for this conference cover several fields of application in life sciences and engineering, as well as in social sciences. Despite the variety of applications, these problems call for common mathematical techniques, and it is therefore fruitful to bring them together in the same conference. These are currently extremely active areas, in the following themes: Integro-differential and lag equations. The fields of application cover multiple living phenomena: population dynamics, modeling of bacterial colonies, spread of infections, ... These equations often involve non-local boundary conditions and include in particular age-structured population models (e.g. McKendrick renewal model). They are in particular studied from the point of view of dynamic systems: linearized or non-linear stability of equilibrium states, highlighting bifurcation phenomena (which translate interesting behaviors from a biological point of view). Reaction-diffusion and cross-diffusion systems. These systems include Keller-Segel type chemotactic systems, which are involved in models of cell aggregation (but also in models of collective population movements in the social sciences), models of epidemic propagation and invasion fronts. in mathematical ecology (and also recent models of rumor propagation on social networks), systems with mass conservation (which are involved in chemical kinetics and biochemistry).

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