The maximum principle is a fundamental tool in the theory of elliptic and parabolic PDE, and stands at the base of the existence and regularity theory of these equations. Since the 1950s this field has been seeing spectacular advances, and many of the great PDE specialists have made it their area of work.

Mostly Maximum Principle started as a relatively small group of high-level mathematicians working in subareas related to the maximum principle, and has expanded in terms of number of participants and subjects such as regularity theory, free boundary problems, degenerate and nonlocal PDEs, minimal surfaces, qualitative properties of solutions, comparison principles and spectral properties, Liouville type results, asymptotic analysis, traveling fronts.

Most of the previous editions were held in Italy (2012 in Rome, 2015 in Agropoli, and 2022 in Cortona), and one was organized in Canada (in 2017 in Banff). The current 5th edition will bring this important event to Latin America for the first time.